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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 December 1 16:44 EST 2021. Contains 349430 sequences. (Running on oeis4.)