%I #21 Apr 15 2021 10:46:57

%S 0,1,8548,5398083,537157696,19076074375,352654485156,4154189102413,

%T 35184646816768,231628411446741,1250002537502500,5743722797690911,

%U 23110548002468928,83177110918426603,272244240093265636,821051189587805625,2305843285702230016,6082649491072763593

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

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

%H Indranil Ghosh, <a href="/A217338/b217338.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (17,-136,680,-2380,6188,-12376,19448,-24310,24310,-19448,12376,-6188,2380,-680,136,-17,1).

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

%F 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]

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

%o (PARI) a(n) = (n^16 + 2*n^4 + 3*n^8 + 2*n^10)/8; \\ _Indranil Ghosh_, Feb 27 2017

%o (Python) def A217338(n): return (n**16 + 2*n**4 + 3*n**8 + 2*n**10)/8 # _Indranil Ghosh_, Feb 27 2017

%Y Row n=4 of A343097.

%Y Cf. A002817, A217331.

%K nonn,easy

%O 0,3

%A _Geoffrey Critzer_, Oct 01 2012