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A277444
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Square array A(n,k) (n>=1, k>=1) read by antidiagonals: A(n,k) is the number of n-colorings of the Möbius ladder M_k on 2k vertices.
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1
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0, 0, 2, 0, 0, 6, 0, 2, 0, 12, 0, 0, 42, 24, 20, 0, 2, 48, 420, 120, 30, 0, 0, 306, 2160, 2420, 360, 42, 0, 2, 600, 17532, 27600, 9750, 840, 56, 0, 0, 2442, 115464, 375260, 191760, 30702, 1680, 72, 0, 2, 6048, 830100, 4810680, 4098510, 917280, 81032, 3024, 90, 0, 0, 20706, 5745120, 62813540, 85691640, 28669662, 3406368, 187560, 5040, 110
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OFFSET
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1,3
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COMMENTS
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M_1 is two vertices connected by a triple edge and thus behaves like the path graph P_2 in terms of colorings. M_2 is isomorphic to K_4, the tetrahedral graph.
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LINKS
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N. L. Biggs, R. M. Damerell and D. A. Sands, Recursive families of graphs, Journal of Combinatorial Theory Series B Volume 12 (1972), 123-131. MR0294172
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FORMULA
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A(n,k) = (n^2-3n+3)^k+(n-1)((3-n)^k-(1-n)^k)-1.
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EXAMPLE
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Square array A(n,k) begins:
0, 0, 0, 0, 0, 0, 0, ...
2, 0, 2, 0, 2, 0, 2, ...
6, 0, 42, 48, 306, 600, 2442, ...
12, 24, 420, 2160, 17532, 115464, 830100, ...
20, 120, 2420, 27600, 375260, 4810680, 62813540, ...
30, 360, 9750, 191760, 4098510, 85691640, 1801468230, ...
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CROSSREFS
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Cf. A277443 (colorings of prism graphs), A182406 (square grid graphs).
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KEYWORD
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AUTHOR
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STATUS
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approved
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