#ComboProject 5
#Taerim Kim, Karnaa Mistry,Weij Zheng
#Results for OddTTT3(3 x (2n+1) TicTacToe that ended in a tie)

#The first 100 Terms of 3 x (2n+1) TicTacToe that ended in a tie
	
[16, 30, 72, 178, 444, 1114, 2808, 7098, 17984, 45656, 116106, 295718, 754226, 1926060, 4924188, 12602416, 32284214, 82777240, 212415744, 545495716, 1401849594, 3604921774, 9275890122, 23881602058, 61518226734, 158548607640, 408814563524, 1054590179342, 2721595930404, 7026452822306, 18147298366496, 46885946293214, 121177055746484, 313283723643176, 810192535596110, 2095874778731180, 5423295440740724, 14037073630916630, 36341276369869088, 94108595062116434, 243758321258056460, 631519064376051686, 1636463783015528228, 4241461650592403456, 10995384407887915850, 28509377078588235950, 73934029147665383810, 191768567416391711378, 497489711804340577094, 1290808418002135615116, 3349716029200174876560, 8694014326320297470602, 22568184767758093670612, 58591510515436877762590, 152136185857947156414468,                         , 1026124031197863134979720, 2665420775385560033259700, 6924434011595832028553478, 17990936569866629738789254, 46749043619248284940474734, 121489767304030414676190000, 315757219492729039889334404, 820752405966688710633771716,                             ,                             , 14422747775610434221867258628, 37503843946764724832205578676, 97531064564428115773980452838, 253657971900639074961709066894, 659768290328323637050051392974, 1716211367368669369337565991114, 4464631297090480673117234899506,                                 ,                                 , 78638331908482305811996031785564, 204636224414985131972158226706042, 532552095247487647350913172553832, 1386028956705664924937925470223324, 3607550497028072085776706817060416, 9390349465828704121851203938718666, 24444414922964772927683533176698954, 63636377842769666442051982776758214, 165675598649863560416814858912812636, 431358476163961907986809540988145060, 1123166739025826203951410611539447370, 2924661977840884857821957219607150644, 7616091047282330225472799987098859670, 19834125236153554572191613966431015468, 51655662991153568927039867938699628114, 134538412518432184484564089012098497720, 350427070534219066714309538314156126256, 912791363387411197976493027945192717998, 2377757006555062323402746829034593778586, 6194197573983466815513394631689996538090, 16137038988794309751784357594762361680478, 42042007088454706141775072412103842254258, 109537653041245766104366386853104680968220, 285406217724774787631551133893043453808524, 743674789356181105708154342619144151152086]

#Time for the computation
0.0620000000

#Recurence for the integer sequence and its initial conditions

(n - 1)*(n - 2)*(235728*n + 3336677)*a(n)/((n + 11)*(272858*n^2 + 3149313*n - 4013249)) - (n - 1)*(670054*n^2 + 8163051*n - 17825750)*a(n + 1)/((n + 11)*(272858*n^2 + 3149313*n - 4013249)) - 2*(74260*n^3 + 2043864*n^2 + 12750889*n - 16728594)*a(n + 2)/((n + 11)*(272858*n^2 + 3149313*n - 4013249)) + (619976*n^3 + 11455318*n^2 + 40566419*n - 57838491)*a(n + 3)/((n + 11)*(272858*n^2 + 3149313*n - 4013249)) + (397196*n^3 + 5585350*n^2 - 3373167*n - 8789391)*a(n + 4)/((n + 11)*(272858*n^2 + 3149313*n - 4013249)) + 2*(74260*n^3 + 2378034*n^2 + 16535578*n - 22626375)*a(n + 5)/((n + 11)*(272858*n^2 + 3149313*n - 4013249)) - (855704*n^3 + 18996255*n^2 + 91842050*n - 133721579)*a(n + 6)/((n + 11)*(272858*n^2 + 3149313*n - 4013249)) + a(n + 7) = 0

a(1) = 16, a(2) = 30, a(3) = 72, a(4) = 178, a(5) = 444, a(6) = 1114, a(7) = 2808