A182789 Number of n-colorings of the 4 X 4 X 4 triangular grid.

0, 0, 0, 6, 2112, 98820, 1574400, 13676250, 80631936, 363204072, 1342218240, 4261697550, 12000120000, 30653510316, 72237215232, 159067919010, 330577363200, 653537970000, 1236951760896, 2253171240342, 3967187906880, 6776444390100, 11264003520000, 18268445544426

Offset

0,4

Comments

The 4 X 4 X 4 triangular grid has 4 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 10 vertices and 18 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 (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Formula

a(n) = n*(n-1)*(n-2)^4*(n^4-9*n^3+31*n^2-49*n+31).

G.f.: -6*x^3*(3267*x^7 +51359*x^6 +195679*x^5 +241075*x^4 +100425*x^3 +12653*x^2 +341*x +1) / (x -1)^11. - Colin Barker, Oct 01 2014

Maple

a:= n-> n^10 -18*n^9 +144*n^8 -672*n^7 +2016*n^6 -4031*n^5 +5368*n^4 -4584*n^3 +2272*n^2 -496*n:
seq(a(n), n=0..30);

Crossrefs

Column k=4 of A182797.

Cf. A178435, A182798, A182788, A182790, A182791, A182792, A182793, A182794, A182795, A182796.

Sequence in context: A373235 A226461 A172943 * A056048 A051113 A067174

Adjacent sequences: A182786 A182787 A182788 * A182790 A182791 A182792

Keyword

nonn,easy

Author

Alois P. Heinz, Dec 02 2010

Status

approved