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A182796
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Number of n-colorings of the 11 X 11 X 11 triangular grid.
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12
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0, 0, 0, 6, 894839431299072, 2669547726944484045356192220, 3453061562403499837458734621479403520, 32534816367748624110581496623513688165161250, 13865643738325095813931525301368809527451487174656, 719243085838104840090332816450418348485262159478161912
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OFFSET
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0,4
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COMMENTS
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The 11 X 11 X 11 triangular grid has 11 rows with k vertices in row k. Each vertex is connected to the neighbors in the same row and up to two vertices in each of the neighboring rows. The graph has 66 vertices and 165 edges altogether.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (67, -2211, 47905, -766480, 9657648, -99795696, 869648208, -6522361560, 42757703560, -247994680648, 1285063345176, -5996962277488, 25371763481680, -97862516286480, 345780890878896, -1123787895356412, 3371363686069236, -9364899127970100, 24151581961607100, -57963796707857040, 129728497393775280, -271250494550621040, 530707489338171600, -972963730453314600, 1673497616379701112, -2703342303382594104, 4105075349580976232, -5864393356544251760, 7886597962249166160, -9989690752182277136, 11923179284862717872, -13413576695470557606, 14226520737620288370, -14226520737620288370, 13413576695470557606, -11923179284862717872, 9989690752182277136, -7886597962249166160, 5864393356544251760, -4105075349580976232, 2703342303382594104, -1673497616379701112, 972963730453314600, -530707489338171600, 271250494550621040, -129728497393775280, 57963796707857040, -24151581961607100, 9364899127970100, -3371363686069236, 1123787895356412, -345780890878896, 97862516286480, -25371763481680, 5996962277488, -1285063345176, 247994680648, -42757703560, 6522361560, -869648208, 99795696, -9657648, 766480, -47905, 2211, -67, 1).
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FORMULA
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a(n) = n^66 -165*n^65 + ... (see Maple program).
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MAPLE
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a:= n-> n^66 -165*n^65 +13430*n^64 -718830*n^63 +28457415*n^62 -888623847*n^61 +22794225600*n^60 -493911980736*n^59 +9226616834936*n^58 -150915853835753*n^57 +2187810200892517*n^56 -28386731631190882*n^55 +332304034158619019*n^54 -3533226535570171926*n^53 +34313909582632869954*n^52 -305856530408381979601*n^51 +2512508789703297897295*n^50 -19089408783899171447224*n^49 +134562619568457264195163*n^48
-882441314560383975170374*n^47 +5396523102436821589146163*n^46 -30840476493483204890335403*n^45 +165009710808610594759616084*n^44 -827914124972290242846288614*n^43 +3900932089129512379033249682*n^42 -17282292209365903724659563631*n^41 +72070311947250436580694965993*n^40 -283166145176179540399078790292*n^39 +1049069241527084408399974095750*n^38 -3667220337345620153484655187124*n^37
+12102613021744672034697503592240*n^36 -37724138339405445177425698342523*n^35 +111095760575994820098618163390207*n^34 -309176068977052084408729303614893*n^33 +813185481965001199040935097964080*n^32 -2021374436814237148012243424806903*n^31 +4748186561462311698450896683155065*n^30 -10537422803434213322732080981201161*n^29 +22086052643134325938087794218181024*n^28
-43699620756746667796067005960087177*n^27 +81574844104346290652888156183655294*n^26 -143561350684851401447755384461673931*n^25 +237980280375008015726322556682052877*n^24 -371206816676060485457461990985198956*n^23 +544170012342342058668596490042636752*n^22 -748657464524219415245225971665770397*n^21 +965053026942268357862711436169935542*n^20 -1163371795450218690971885318270471694*n^19
+1308697520027710079307786302348771339*n^18 -1370319041971898252774123231153226918*n^17 +1331690339384350939067376866415236621*n^16 -1197068569703716329028295302490292938*n^15 +991428141596470240524919848774681738*n^14 -753054945934102362521837371999863872*n^13 +521731607147367465356546993487963024*n^12 -327563800253835254381288187488707872*n^11 +184908996556501805959894731292086336*n^10
-92949398227453879699243734196772032*n^9 +41108507052047410428558518243062272*n^8 -15751620136596962785464735723309056*n^7 +5123987337580699585298644858115072*n^6 -1376145015411556644420090237028352*n^5 +292997762191812894902503923634176*n^4 -46372215676408895763951507652608*n^3 +4850060647318928018465677025280*n^2 -251433237032021534887746912256*n:
seq(a(n), n=0..12);
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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