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 A182795 Number of n-colorings of the Triangle Graph of order 10. 12
 0, 0, 0, 6, 6468240187392, 143635721907943000938060, 4861091521972177266672058368000, 2856800670438221106476061284736341250, 131028911804088893672445293407292154494976 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS The Triangle Graph of order 10 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. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 Eric Weisstein's World of Mathematics, Triangle Graph Wikipedia, Chromatic polynomial FORMULA a(n) = n^55 -135*n^54 + ... (see Maple program). MAPLE 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); CROSSREFS 10th column of A182797. Cf. A178435, A182798, A182788, A182789, A182790, A182791, A182792, A182793, A182794, A182796. Sequence in context: A058457 A182794 A072240 * A182796 A079683 A115528 Adjacent sequences:  A182792 A182793 A182794 * A182796 A182797 A182798 KEYWORD nonn AUTHOR Alois P. Heinz, Dec 02 2010 STATUS approved

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Last modified October 23 17:19 EDT 2019. Contains 328373 sequences. (Running on oeis4.)