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A047937
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Number of 2-colorings of an n X n grid, up to rotational symmetry.
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10
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1, 2, 6, 140, 16456, 8390720, 17179934976, 140737496748032, 4611686019501162496, 604462909807864344215552, 316912650057057631849169289216, 664613997892457937028364283517337600
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Cycle index = 1/4(s_1^(n^2)+ 2 s_4^floor(n^2/4)s_1^(n mod 2)+s_2^floor(n^2/2)s_1^(n mod 2)). - Geoffrey Critzer, Oct 28 2011
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FORMULA
| a(n) = (m^(n^2) + 2 m^((n^2 + 3 (n mod 2))/4) + m^((n^2 + (n mod 2))/2))/4, with m = 2
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EXAMPLE
| a(2)=6 from
00 10 11 10 11 11
00 00 00 01 10 11
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MATHEMATICA
| Table[(2^(n^2)+2*2^Floor[n^2/4]*2^Mod[n, 2]+2^Floor[n^2/2]*2^Mod[n, 2])/4, {n, 0, 10}] (* Geoffrey Critzer, Oct 28 2011 *)
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CROSSREFS
| Cf. A054247, A047937-A047945.
Sequence in context: A156515 A090907 A159478 * A027731 A145143 A164764
Adjacent sequences: A047934 A047935 A047936 * A047938 A047939 A047940
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KEYWORD
| nonn,easy,nice
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AUTHOR
| Robert W. Pratt (Rob.Pratt(AT)sas.com)
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