A182794 Number of n-colorings of the 9 X 9 X 9 triangular grid.

0, 0, 0, 6, 67849629696, 17497810918123218900, 21925009706068920874598400, 1045584233565048659578102256250, 6368832392862110714579731514351616, 9534235558912413569697852308677120776

Offset

0,4

Comments

The 9 X 9 X 9 triangular grid has 9 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 45 vertices and 108 edges altogether.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Wikipedia, Chromatic polynomial

Wikipedia, Triangular grid graph

Index entries for linear recurrences with constant coefficients, signature (46, -1035, 15180, -163185, 1370754, -9366819, 53524680, -260932815, 1101716330, -4076350421, 13340783196, -38910617655, 101766230790, -239877544005, 511738760544, -991493848554, 1749695026860, -2818953098830, 4154246671960, -5608233007146, 6943526580276, -7890371113950, 8233430727600, -7890371113950, 6943526580276, -5608233007146, 4154246671960, -2818953098830, 1749695026860, -991493848554, 511738760544, -239877544005, 101766230790, -38910617655, 13340783196, -4076350421, 1101716330, -260932815, 53524680, -9366819, 1370754, -163185, 15180, -1035, 46, -1).

Formula

a(n) = n^45 -108*n^44 + ... (see Maple program).

Maple

a:= n-> n^45 -108*n^44 +5714*n^43 -197372*n^42 +5004951*n^41 -99331939*n^40 +1606376002*n^39 -21760175421*n^38+251900492473*n^37 -2529947375509*n^36 +22305591797446*n^35 -174257688976920*n^34 +1215408574487125*n^33 -7615215090082277*n^32 +43080094524111690*n^31 -220967851371444614*n^30 +1031210769134504204*n^29 -4391099235591937845*n^28 +17100876656070073880*n^27 -61022823409833058201*n^26
+199812365243382363912*n^25 -600991376049390898992*n^24 +1661619908871238912196*n^23 -4224371709444972487708*n^22 +9875485316923894342417*n^21 -21221061699176359482887*n^20 +41886723683404956818991*n^19 -75858892195631057087330*n^18 +125862045971633675717554*n^17 -190930468100539717386672*n^16 +264149971345371552591904*n^15 -332242305634477726845448*n^14 +378446023463873654411519*n^13
-388532455150677959308540*n^12 +357418193476328504707252*n^11 -292480744218652691170096*n^10 +210981642121913298294408*n^9 -132621489649268878766112*n^8 +71568787087815309389792*n^7 -32504434438954975091968*n^6 +12087094618713177654080*n^5 -3534893963007018617856*n^4 +762559875649969442816*n^3 -107896190008663345152*n^2 +7511367180771568640*n: seq(a(n), n=0..12);

Crossrefs

9th column of A182797. Cf. A178435, A182798, A182788, A182789, A182790, A182791, A182792, A182793, A182795, A182796.

Sequence in context: A058431 A045518 A058457 * A072240 A182795 A182796

Adjacent sequences: A182791 A182792 A182793 * A182795 A182796 A182797

Keyword

nonn,easy

Author

Alois P. Heinz, Dec 02 2010

Status

approved