{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 } {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 65 " \+ Magilatin affine count" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 90 "COMPUTE: the number of magilatin squares with magic sum e qual to t, for small values of t." }}{PARA 0 "" 0 "" {TEXT -1 172 "MET HOD: generate all weakly magilatin positive squares and eliminate thos e that have repeated values in a row or column. This is the stupid me thod; there are no shortcuts." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 101 "Notation: the 3x3 square is x, with cells numbered from 1 to 9 across rows, starting at the top left." }}{PARA 0 "" 0 "" {TEXT -1 37 "The v alues of t range from 1 to tmax." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "tmax:=100;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%tmaxG\"$+\"" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 59 "The generating function, computed \+ in another Maple program." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 318 "Lgf : = -12*x^6*(1+3*x+676*x^11+33*x^4+7*x^2+434*x^9+852*x^13+15*x^3+316*x^8 +65*x^5+128*x^6+208*x^7+1001*x^18+79*x^28+967*x^16+784*x^12+624*x^24+9 95*x^19+955*x^21+1000*x^20+936*x^15+967*x^17+893*x^22+456*x^25+174*x^2 7+911*x^14+322*x^26+752*x^23+566*x^10)/(x^3-1)/(x+1)/(x^7-1)/(x^6-1)/( x^8-1)/(x^5-1)/(x^2+x+1)/(x^2+1);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#> %$LgfG,$*8\"#7\"\"\"%\"xG\"\"',fnF(F(*&\"\"$F(F)F(F(*&\"$w'F()F)\"#6F( F(*&\"$%yF()F)F'F(F(*&\"$n*F()F)\"#;F(F(*&\"#zF()F)\"#GF(F(*&\"%,5F()F )\"#=F(F(*&\"$3#F()F)\"\"(F(F(*&\"#lF()F)\"\"&F(F(*&\"$;$F()F)\"\")F(F (*&\"#:F()F)F-F(F(*&\"$_)F()F)\"#8F(F(*&\"$M%F()F)\"\"*F(F(*&FDF()F)\" \"#F(F(*&\"#LF()F)\"\"%F(F(*&\"$G\"F()F)F*F(F(*&\"$m&F()F)\"#5F(F(*&\" $_(F()F)\"#BF(F(*&\"$A$F()F)\"#EF(F(*&\"$6*F()F)\"#9F(F(*&\"$u\"F()F) \"#FF(F(*&\"$c%F()F)\"#DF(F(*&\"$$*)F()F)\"#AF(F(*&F6F()F)\"#F(F(*&\"$C'F()F)\"#CF(F(F(,&*$FOF(F(F(!\"\"F`r,&F)F(F(F(F`r,&*$FCF(F( F(F`rF`r,&*$F[oF(F(F(F`rF`r,&*$FKF(F(F(F`rF`r,&*$FGF(F(F(F`rF`r,(*$FYF (F(F)F(F(F(F`r,&F[sF(F(F(F`rF`r" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1206 "for t from 1 to tmax do\n count[t]:=0:\n for x[1] from 1 to \+ t-3 do\n for x[2] from 1 to t-x[1]-1 do \n x[3]:=t-x[1]-x[2]:\n i f( x[1]=x[2] or x[3]=x[1] or x[3]=x[2] ) then \n else \n for x[4 ] from 1 to t-x[1]-1 do\n if( x[4]=x[1] ) then \n else\n \+ x[7]:=t-x[1]-x[4]:\n if( x[7]=x[1] or x[7]=x[4] ) then \n \+ else\n x5bound:=t-1-max(x[2],x[4]);\n for x[5] from max(1,x[3]-x[4]+1) to x5bound do\n if( x[5]=x[2] or x [5]=x[4] ) then \n else \n ok:=1: \n \+ x[6]:=t-x[5]-x[4]:\n x[8]:=t-x[5]-x[2]:\n x[ 9]:=t-x[3]-x[6]:\n if( x[8]=x[5] or x[8]=x[2] or x[8]=x[7] ) then \n ok:=0: \n fi:\n if( \+ x[6]=x[5] or x[6]=x[4] or x[6]=x[3] ) then\n ok:=0:\n \+ fi:\n if( x[9]=x[6] or x[9]=x[3] or x[9]=x[8] or x[9]=x[7] ) then\n ok:=0:\n fi:\n \+ count[t]:=count[t]+ok:\n fi:\n od:\n fi: \n fi:\n od:\n fi:\n od:\n od: \n Lc[t]:=coeff(series(Lgf, x=0,tmax+1),x^t):\n if( count[t]=Lc[t] ) then print(t,count[t],\"Consi stent\");\n else print(t,count[t],Lc[t],\"Inconsistency\"); \n fi: \n od:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"\"\"\"!Q+Consistent6\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"#\"\"!Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"$\"\"!Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"%\"\"!Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"&\"\"!Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\" \"'\"#7Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"(\"#7Q+C onsistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\")\"#CQ+Consistent6 \"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"*\"#sQ+Consistent6\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "6%\"#5\"$c\"Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#6\"$S#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 \"%?5Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#:\"%[:Q+Con sistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#;\"%/?Q+Consistent6\" " }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#<\"%oDQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#=\"%3SQ+Consistent6\"" }}{PARA 11 "" 1 " " {XPPMATH 20 "6%\"#>\"%WYQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#?\"%kiQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#@\"%O\")Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\" #A\"&_,\"Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#B\"&o@ \"Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#C\"&%G;Q+Consi stent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#D\"&s$=Q+Consistent6\" " }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#E\"&#*H#Q+Consistent6\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "6%\"#F\"&sz#Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#G\"&OF$Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#H\"&'*y$Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#I\"&_t%Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#J\"&KB&Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"# K\"&/?'Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#L\"&)GsQ+ Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#M\"&sD)Q+Consisten t6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#N\"&3J*Q+Consistent6\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "6%\"#O\"'!G5\"Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#P\"'#\\?\"Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#Q\"'?%Q\"Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#R\"'Gu:Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#S\"'[_Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#U\"'GMAQ+ Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#V\"'+:CQ+Consisten t6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#W\"'W2FQ+Consistent6\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "6%\"#X\"';)*Q+Consistent6\"" }}}{EXCHG }}{MARK "6" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }