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A182795
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Number of n-colorings of the 10 X 10 X 10 triangular grid.
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12
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0, 0, 0, 6, 6468240187392, 143635721907943000938060, 4861091521972177266672058368000, 2856800670438221106476061284736341250, 131028911804088893672445293407292154494976
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OFFSET
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0,4
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COMMENTS
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The 10 X 10 X 10 triangular grid has 10 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 55 vertices and 135 edges altogether.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (56, -1540, 27720, -367290, 3819816, -32468436, 231917400, -1420494075, 7575968400, -35607051480, 148902215280, -558383307300, 1889912732400, -5804731963800, 16253249498640, -41648951840265, 97997533741800, -212327989773900, 424655979547800, -785613562163430, 1346766106565880, -2142582442263900, 3167295784216200, -4355031703297275, 5574440580220512, -6646448384109072, 7384942649010080, -7648690600760440, 7384942649010080, -6646448384109072, 5574440580220512, -4355031703297275, 3167295784216200, -2142582442263900, 1346766106565880, -785613562163430, 424655979547800, -212327989773900, 97997533741800, -41648951840265, 16253249498640, -5804731963800, 1889912732400, -558383307300, 148902215280, -35607051480, 7575968400, -1420494075, 231917400, -32468436, 3819816, -367290, 27720, -1540, 56, -1).
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FORMULA
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a(n) = n^55 -135*n^54 + ... (see Maple program).
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MAPLE
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a:= n-> n^55 -135*n^54 +8964*n^53 -390222*n^52 +12525057*n^51 -316076903*n^50 +6530286070*n^49 -113573987769*n^48 +1696787220520*n^47 -22113112510550*n^46 +254428951045842*n^45 -2609511250718613*n^44 +24045856082285419*n^43 -200371113856491240*n^42 +1518133675627952270*n^41 -10506651071221868153*n^40 +66680463251797921915*n^39 -389373183471975572302*n^38 +2098028797385404193010*n^37
-10456871082871436486097*n^36 +48311408769374448761586*n^35 -207268123118278617037243*n^34 +827002152243388922174239*n^33 -3072694198727638003487979*n^32 +10641864949286796056022377*n^31 -34383949683339954923684782*n^30 +103704885062207595279156312*n^29 -292098504456226533053440510*n^28 +768501708532085822533190556*n^27 -1888698433570434475839725929*n^26 +4335279422341414825800378209*n^25
-9290907905051445440799000716*n^24 +18580084162229028469273798451*n^23 -34646102938311786771803477712*n^22 +60179271229381177090538625964*n^21 -97248893234106206859587981511*n^20 +145984266730291101055714541723*n^19 -203195282517216004808829603690*n^18 +261670683045031491886557091942*n^17 -310956138275834795608083550274*n^16 +339941943100528554861813262560*n^15
-340628682378318048979653175381*n^14 +311484260127833509262781795600*n^13 -258586709722348835998646850788*n^12 +193670730551369756737363762352*n^11 -129863868693889627423240097464*n^10 +77228998619164716149657770512*n^9 -40252487790410927197535447840*n^8 +18109784947870880558334595968*n^7 -6892748007729626216676319168*n^6 +2158618972888431826460898944*n^5 -534180587663008964293559296*n^4
+97953970795833012084624384*n^3 -11833494445627750018634752*n^2 +706434229524151535286272*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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