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A217338 Number of inequivalent ways to color a 4 X 4 checkerboard using at most n colors allowing rotations and reflections. 3
0, 1, 8548, 5398083, 537157696, 19076074375, 352654485156, 4154189102413, 35184646816768, 231628411446741, 1250002537502500, 5743722797690911, 23110548002468928, 83177110918426603, 272244240093265636, 821051189587805625, 2305843285702230016, 6082649491072763593 (list; graph; refs; listen; history; text; internal format)
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
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.
Sequence in context: A252810 A202986 A297896 * A217163 A243839 A287119
KEYWORD
nonn,easy
AUTHOR
Geoffrey Critzer, Oct 01 2012
STATUS
approved

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Last modified May 21 00:14 EDT 2024. Contains 372720 sequences. (Running on oeis4.)