{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 }} {SECT 0 {PARA 3 "" 0 "" {TEXT -1 66 " Cubic count of semim agic 3x3 squares (by upper bound)" }}{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 period)." }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "step:=1:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 65 "The generating function of semimagic squares, computed el sewhere." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 113 "Sgf:=72*x^10*(18*x^9+4 6*x^8+69*x^7+74*x^6+65*x^5+46*x^4+26*x^3+11*x^2+4*x+1)/(x^2-1)^2/(x^3- 1)^2/(x^5-1)/(x^4-1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$SgfG,$*0\" #s\"\"\"%\"xG\"#5,6*&\"#=F()F)\"\"*F(F(*&\"#YF()F)\"\")F(F(*&\"#pF()F) \"\"(F(F(*&\"#uF()F)\"\"'F(F(*&\"#lF()F)\"\"&F(F(*&F1F()F)\"\"%F(F(*& \"#EF()F)\"\"$F(F(*&\"#6F()F)\"\"#F(F(*&FBF(F)F(F(F(F(F(,&*$FIF(F(F(! \"\"!\"#,&*$FEF(F(F(FNFO,&*$F>F(F(F(FNFN,&*$FAF(F(F(FNFNF(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 256 28 "Semimagic cubic 3x3 squares" }}{PARA 0 "" 0 "" {TEXT -1 100 "We calculate the number of strongly semimagic (S c[k]) and normal strongly semimagic (sc[k]) squares." }}{PARA 0 "" 0 " " {TEXT -1 265 "This is the raw data calculated by a simple method wit h symmetry used to reduce the computation. The symmetries are: first \+ row and column in increasing order, and top side square greater than l eft side square (the opposite of the normalization in the article SLS) ." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 350 "for k from mink to maxk by st ep do \n sc[k]:=0: \n for x[1] from 1 to k-1 do\n for x[2] from x[ 1]+1 to k-1 do \n for x[3] from x[2]+1 to k-1 do \n magicsum :=x[1]+x[2]+x[3]: \n for x[4] from x[1]+1 to x[2]-1 do \n \+ x[7]:=magicsum-x[1]-x[4]: \n if ( (x[7]>x[4]) and (x[7] " 0 " " {MPLTEXT 1 0 415 " x[6]:=magicsum-x[4]-x[5]:\n x [8]:=magicsum-x[2]-x[5]: \n x[9]:=magicsum-x[3]-x[6]: \n \+ if ( (x[6]>x[1]) and (x[8]>x[1]) and (x[9]>x[1]) and (x[6] " 0 "" {MPLTEXT 1 0 354 " \+ eq:= eq or (x[4]=x[3]) or (x[5]=x[1]) or (x[5]=x[3]) or (x[6]=x[1]) \+ or (x[6]=x[2]) or (x[7]=x[1]) or (x[7]=x[2]) or (x[7]=x[3]) or (x[7]=x [4]) or (x[7]=x[5]) or (x[7]=x[6]) or (x[8]=x[1]) or (x[8]=x[3]) or (x [8]=x[4]) or (x[8]=x[6]) or (x[9]=x[1]) or (x[9]=x[2]) or (x[9]=x[4]) \+ or (x[9]=x[5]):\n if not eq then sc[k]:=sc[k]+1: fi:" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 " fi:\n od:\n \+ fi:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 206 " od:\n od: \+ \n od:\n od:\n Sc[k]:=72*sc[k]: \n S[k]:=coeff(series(Sgf,x=0,max k+1),x^k): \n if( Sc[k]=S[k] ) then print(k,Sc[k],\"Consistent\"):\n \+ else print(k,Sc[k],S[k],\"Inconsistent\"): \n fi: \nod:" }}{PAGEBK }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\" \"\"\"!Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"#\"\"!Q+ Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"$\"\"!Q+Consisten t6\"" }}{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\"#sQ+C onsistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#6\"$)GQ+Consistent6 \"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#7\"$O*Q+Consistent6\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "6%\"#8\"%#f#Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#9\"%gdQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#:\"&?:\"Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#;\"&_4#Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#<\"&7d$Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"# =\"&or&Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#>\"&s#))Q +Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#?\"'768Q+Consiste nt6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#@\"'/&*=Q+Consistent6\"" } }{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#A\"'_dEQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#B\"'gdOQ+Consistent6\"" }}{PARA 11 "" 1 " " {XPPMATH 20 "6%\"#C\"'![#\\Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#D\"'SIlQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#E\"'s9&)Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\" #F\"(;k4\"Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#G\"(oF R\"Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#H\"(/>v\"Q+Co nsistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#I\"(k)y@Q+Consistent 6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#J\"(%=(o#Q+Consistent6\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "6%\"#K\"(KOG$Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#L\"(gP)RQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#M\"(%)\\z%Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#N\"(Glt&Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#O\"(ck\"oQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#P\"(Ci0)Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#Q\"(GhY*Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#R\")K/26Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#S\")_,)G\"Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#T\");S#\\\"Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#U\")GL@Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#W\")W(QE#Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#X\")_R#e#Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#Y\")G2NHQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#Z\")#RfK$Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#[\")cecPQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#\\\")oRJUQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#]\")#fAv%Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#^\")[#RK&Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#_\")kO[fQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#`\")S)4j'Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#a\")C#QP(Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#b\")[o#=)Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#c\")[+g!*Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#d\"*+'>,5Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#e\"*w2T5\"Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#f\"*cIa@\"Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#g\"*/DaL\"Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#h\"*#*H[Y\"Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#i\"*WXRg\"Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#j\"*ceNv\"Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#k\"*[#)R\">Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#l\"*![3'3#Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#m\"*#f=qAQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#n\"*%Q?nCQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#o\"*O4vn#Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#p\"*)32-HQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#q\"*7n79$Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#r\"*!3;'R$Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#s\"*+Srm$Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#t\"*)GKbRQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#u\"*3]6E%Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#v\"*?&z&e%Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#w\"*%=rH\\Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#x\"*'H<%H&Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#y\"*CU'zcQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#z\"*+cu3'Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#!)\"*_N\"=lQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#\")\"*;wI(pQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"##)\"*c3GX(Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#$)\"*cU)ezQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#%)\"*[A<\\)Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#&)\"*!3-`!*Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#')\"*/VLk*Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#()\"+?FVE5Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#))\"+k%f;4\"Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#*)\"+K/>g6Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#!*\"+C')3K7Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#\"*\"+Or`28Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"##*\"+Odg'Q\"Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#$*\"+wX[p9Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#%*\"+#zWib\"Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#&*\"+o&*3Z;Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#'*\"+394UQ+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"#**\"+!ofP0#Q+Consistent6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"$+\"\"+_())p;#Q+Consistent6\"" }}}{EXCHG }}{MARK "4 9 4 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }