A217338 Number of inequivalent ways to color a 4 X 4 checkerboard using at most n colors allowing rotations and reflections.

0, 1, 8548, 5398083, 537157696, 19076074375, 352654485156, 4154189102413, 35184646816768, 231628411446741, 1250002537502500, 5743722797690911, 23110548002468928, 83177110918426603, 272244240093265636, 821051189587805625, 2305843285702230016, 6082649491072763593

Offset

0,3

Comments

Cycle index of symmetry group: (s(1)^16 + 2*s(4)^4 + 3*s(2)^8 + 2*s(2)^6*s(1)^4)/8.

Links

Indranil Ghosh, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (17,-136,680,-2380,6188,-12376,19448,-24310,24310,-19448,12376,-6188,2380,-680,136,-17,1).

Formula

a(n) = (n^16 + 2*n^4 + 3*n^8 + 2*n^10)/8.

G.f.: -x*(x +1)*(x^14 +8530*x^13 +5244373*x^12 +441307760*x^11 +10231414811*x^10 +87532894238*x^9 +313403397135*x^8 +484445834304*x^7 +313403397135*x^6 +87532894238*x^5 +10231414811*x^4 +441307760*x^3 +5244373*x^2 +8530*x +1)/(x -1)^17. [Colin Barker, Oct 04 2012]

Mathematica

Table[(n^16+2n^4+3n^8+2n^10)/8, {n, 0, 20}]

Prog

(PARI) a(n) = (n^16 + 2*n^4 + 3*n^8 + 2*n^10)/8; \\ Indranil Ghosh, Feb 27 2017
(Python) def A217338(n): return (n**16 + 2*n**4 + 3*n**8 + 2*n**10)/8 # Indranil Ghosh, Feb 27 2017

Crossrefs

Row n=4 of A343097.

Cf. A002817, A217331.

Sequence in context: A252810 A202986 A297896 * A217163 A243839 A287119

Adjacent sequences: A217335 A217336 A217337 * A217339 A217340 A217341

Keyword

nonn,easy

Author

Geoffrey Critzer, Oct 01 2012

Status

approved