A182792 Number of n-colorings of the 7 X 7 X 7 triangular grid.

0, 0, 0, 6, 22665216, 3013780700340, 14668353488732160, 10142843465859326250, 2047585083571827265536, 177922459478738381782536, 8379024937788205785415680, 247855358008532074713890670, 5089690042011600555045120000

Offset

0,4

Comments

The 7 X 7 X 7 triangular grid has 7 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 28 vertices and 63 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 (29, -406, 3654, -23751, 118755, -475020, 1560780, -4292145, 10015005, -20030010, 34597290, -51895935, 67863915, -77558760, 77558760, -67863915, 51895935, -34597290, 20030010, -10015005, 4292145, -1560780, 475020, -118755, 23751, -3654, 406, -29, 1).

Formula

a(n) = n^28 -63*n^27 + ... (see Maple program).

Maple

a:= n-> n^28 -63*n^27 +1917*n^26 -37515*n^25 +530415*n^24 -5770367*n^23 +50229001*n^22 -359161581*n^21 +2149154827*n^20 -10907730408*n^19 +47421892719*n^18 -177879720291*n^17 +578605822984*n^16 -1637514420168*n^15 +4039146735437*n^14 -8685828617404*n^13 +16263806276269*n^12 -26442885506316*n^11 +37160408393135*n^10 -44834641208000*n^9 +46004737388704*n^8 -39623922744400*n^7
+28128173982016*n^6 -16032767219808*n^5 +7056432341248*n^4 -2251430597120*n^3 +463382611200*n^2 -46172626432*n: seq(a(n), n=0..30);

Crossrefs

7th column of A182797. Cf. A178435, A182798, A182788, A182789, A182790, A182791, A182793, A182794, A182795, A182796.

Sequence in context: A269516 A116272 A273723 * A067484 A337083 A363500

Adjacent sequences: A182789 A182790 A182791 * A182793 A182794 A182795

Keyword

nonn,easy

Author

Alois P. Heinz, Dec 02 2010

Status

approved