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

Author

Geoffrey Critzer, Oct 01 2012

Keywords

• nonn
• easy

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).

Crossrefs

Row n=4 of A343097.

Cf. A002817, A217331.

Programs

Mathematica

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

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

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 [phone]*x^11 [phone]*x^10 [phone]*x^9 [phone]*x^8 [phone]*x^7 [phone]*x^6 [phone]*x^5 [phone]*x^4 [phone]*x^3 +5244373*x^2 +8530*x +1)/(x -1)^17. [Colin Barker, Oct 04 2012]