{VERSION 6 0 "IBM INTEL LINUX" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 256 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 }{PSTYLE "Normal " -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }1 0 0 0 8 4 0 0 0 0 0 0 -1 0 } {PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG }{PARA 3 "" 0 "" {TEXT -1 67 " Count \+ of normal and all affine semimagic squares" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 51 "Minimum and maximum value of k in all calculations." }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "mink:=1: maxk:=100:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 46 "Step size (this could be 1 or a trial per iod)." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "step:=1:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 65 "The generating function of semimagic squares, c omputed elsewhere." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 233 "Sgf:=-72*x^1 5*(18*x^19+41*x^18+79*x^17+117*x^16+166*x^15+207*x^14+249*x^13+268*x^1 2+274*x^11+258*x^10+233*x^9+192*x^8+152*x^7+109*x^6+73*x^5+44*x^4+24*x ^3+11*x^2+4*x+1)/(x^7-1)/(x^6-1)/(x^8-1)/(x^5-1)/(x^2+x+1)/(x^3-1)/(x^ 3+x^2+x+1);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$SgfG,$*6\"#s\"\"\"% \"xG\"#:,J*&\"#=F()F)\"#>F(F(*&\"#TF()F)F-F(F(*&\"#zF()F)\"#F()F)\"\")F(F(*&\"$_\"F()F)\"\"(F(F(*&\"$4\"F( )F)\"\"'F(F(*&\"#tF()F)\"\"&F(F(*&\"#WF()F)\"\"%F(F(*&\"#CF()F)\"\"$F( F(*&FMF()F)\"\"#F(F(*&FcoF(F)F(F(F(F(F(,&*$FfnF(F(F(!\"\"F^p,&*$FjnF(F (F(F^pF^p,&*$FXF(F(F(F^pF^p,&*$F^oF(F(F(F^pF^p,(*$FioF(F(F)F(F(F(F^p,& *$FfoF(F(F(F^pF^p,*FhpF(FfpF(F)F(F(F(F^pF^p" }}}{EXCHG {PARA 0 "" 0 " " {TEXT 256 30 "Semimagic affine 3x3 squares" }}{PARA 0 "" 0 "" {TEXT -1 153 "We calculate the number of strongly semimagic (Sa[k]) an d normal strongly semimagic (sa[k]) squares and check it against the g enerating function (Sgf). " }}{PARA 0 "" 0 "" {TEXT -1 258 "This is t he raw data calculated by a simple method with symmetry used to reduce the computation. The symmetries are: first row and column in increas ing order, and top side square greater than left side square (opposite to the convention in the article SLS)." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 320 "for k from mink to maxk by step do \n sa[k]:=0: \n for x[1] from 1 to (k-2) do\n for x[2] from (x[1]+1) to (k-1) do \n x[3] :=k-x[1]-x[2]:\n if ( x[3]>x[2] ) then \n for x[4] from (x[1 ]+1) to (x[2]-1) do \n x[7]:=k-x[1]-x[4]: \n if ( (x[7 ]>x[4]) ) then\n for x[5] from x[1]+1 to (k-1) do " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 355 " x[6]:=k-x[4]-x[5]:\n \+ x[8]:=k-x[2]-x[5]: \n x[9]:=k-x[3]-x[6]: \n if ( ( x[6]>x[1]) and (x[8]>x[1]) and (x[9]>x[1]) ) then \n eq:= \+ (x[5]=x[2]) or (x[5]=x[4]) or (x[6]=x[3]) or (x[6]=x[4]) or (x[6]=x[5] ) or (x[8]=x[2]) or (x[8]=x[5]) or (x[8]=x[7]) or (x[9]=x[3]) or (x[9] =x[6]) or (x[9]=x[7]) or (x[9]=x[8]):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 354 " eq:= eq or (x[4]=x[3]) or (x[5]=x[1]) or (x[5]=x[3 ]) or (x[6]=x[1]) or (x[6]=x[2]) or (x[7]=x[1]) or (x[7]=x[2]) or (x[7 ]=x[3]) or (x[7]=x[4]) or (x[7]=x[5]) or (x[7]=x[6]) or (x[8]=x[1]) or (x[8]=x[3]) or (x[8]=x[4]) or (x[8]=x[6]) or (x[9]=x[1]) or (x[9]=x[2 ]) or (x[9]=x[4]) or (x[9]=x[5]):\n if not eq then sa[k]:= sa[k]+1: fi:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 40 " fi:\n \+ od:\n fi:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 206 " \+ od:\n fi: \n od:\n od:\n Sa[k]:=72*sa[k]: \n S[k]:=coeff(seri es(Sgf,x=0,maxk+1),x^k): \n if( Sa[k]=S[k] ) then print(k,Sa[k],\"Con sistent\"):\n else print(k,Sa[k],S[k],\"Inconsistent\"): \n fi: \no d:" }}{PAGEBK }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"\"\"\"!Q+Consi stent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"#\"\"!Q+Consistent6\" " }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"$\"\"!Q+Consistent6\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"%\"\"!Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"&\"\"!Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"'\"\"!Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"(\"\"!Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\" \")\"\"!Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"*\"\"!Q +Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#5\"\"!Q+Consisten t6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#6\"\"!Q+Consistent6\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "6%\"#7\"\"!Q+Consistent6\"" }}{PARA 11 " " 1 "" {XPPMATH 20 "6%\"#8\"\"!Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#9\"\"!Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#:\"#sQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#; \"$W\"Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#<\"$)GQ+Co nsistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#=\"$w&Q+Consistent6 \"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#>\"$k)Q+Consistent6\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "6%\"#?\"%S9Q+Consistent6\"" }}{PARA 11 " " 1 "" {XPPMATH 20 "6%\"#@\"%)3#Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#A\"%CIQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#B\"%))QQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"# C\"%/fQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#D\"%%)pQ+C onsistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#E\"%K%*Q+Consistent 6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#F\"&o@\"Q+Consistent6\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "6%\"#G\"&/\\\"Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#H\"&Gz\"Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#I\"&KQ#Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#J\"&%yEQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#K\"&[I$Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"# L\"&s'RQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#M\"&%eYQ+ Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#N\"&SO&Q+Consisten t6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#O\"&#flQ+Consistent6\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "6%\"#P\"&/D(Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#Q\"&[_)Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#R\"&G*)*Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#S\"';=6Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#T\"'3_7Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"# U\"'Gv9Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#V\"'K1;Q+ Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#W\"'3G=Q+Consisten t6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#X\"'Ck?Q+Consistent6\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "6%\"#Y\"'w\"H#Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#Z\"'[EDQ+Consistent6\"" }}{PARA 11 "" 1 " " {XPPMATH 20 "6%\"#[\"'GzGQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#\\\"'_2JQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#]\"'SqMQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#^\"'![%QQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\" #_\"'?,UQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#`\"'+sXQ +Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#a\"')[6&Q+Consist ent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#b\"'/xaQ+Consistent6\"" } }{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#c\"'W8gQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#d\"'/vlQ+Consistent6\"" }}{PARA 11 "" 1 " " {XPPMATH 20 "6%\"#e\"'/:rQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#f\"'sowQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#g\"'GT%)Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\" #h\"'%)z*)Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#i\"'sc (*Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#j\"(Od0\"Q+Con sistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#k\"(%)>8\"Q+Consisten t6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#l\"(_2@\"Q+Consistent6\"" } }{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#m\"(/\"=8Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#n\"(s]R\"Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#o\"(74]\"Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#p\"(%y5;Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#q\"(Cmr\"Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#r\"(CY#=Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#s\"(%=n>Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#t\"(#fs?Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#u\"(C_@#Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#v\"(%QhBQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#w\"(O6]#Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#x\"(k]k#Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#y\"()oJGQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#z\"([C(HQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#!)\"(Cm:$Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#\")\"(+iM$Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"##)\"(o$HNQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#$)\"(?fr$Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#%)\"(GF&RQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#&)\"(3c8%Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#')\"(k7P%Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#()\"(#R7YQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#))\"()3W[Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#*)\"(+93&Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#!*\"(w*y`Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#\"*\"(3;h&Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"##*\"(!30fQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#$*\"('*e?'Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#%*\"(Or\\'Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#&*\"(/Pz'Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#'*\"(c%erQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#(*\"(O$\\uQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#)*\"(W@\"yQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#**\"(!3#=)Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"$+\"\"(G\"R&)Q+Consistent6\"" }}}{EXCHG }{EXCHG } {EXCHG }}{MARK "4 1 0" 233 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 } {PAGENUMBERS 0 1 2 33 1 1 }