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A277443 Square array A(n,k) (n>=1, k>=1) read by antidiagonals: A(n,k) is the number of n-colorings of the prism graph Y_k on 2k vertices. 1
0, 0, 0, 0, 2, 0, 0, 0, 18, 0, 0, 2, 12, 84, 0, 0, 0, 114, 264, 260, 0, 0, 2, 180, 2652, 1920, 630, 0, 0, 0, 858, 16080, 29660, 8520, 1302, 0, 0, 2, 1932, 119844, 367080, 198030, 28140, 2408, 0, 0, 0, 7074, 816984, 4843460, 4067280, 932862, 76272, 4104, 0, 0, 2, 18660, 5784492, 62682480, 85847910, 28576380, 3440024, 179424, 6570, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Y_1 contains a loop, so has no colorings with any number of colors. Y_2 is the cycle graph C_4 with two double edges; these two graphs are therefore equivalent with respect to number of colorings.

LINKS

Table of n, a(n) for n=1..66.

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

Eric Weisstein's World of Mathematics, Prism Graph

Wikipedia, Chromatic polynomial

FORMULA

A(n,k) = (n^2-3n+3)^k+(n-1)((3-n)^k+(1-n)^k)+n^2-3n+1.

EXAMPLE

Square array A(n,k) begins:

  0,   0,    0,      0,       0,        0,          0, ...

  0,   2,    0,      2,       0,        2,          0, ...

  0,  18,   12,    114,     180,      858,       1932, ...

  0,  84,  264,   2652,   16080,   119844,     816984, ...

  0, 260, 1920,  29660,  367080,  4843460,   62682480, ...

  0, 630, 8520, 198030, 4067280, 85847910, 1800687000, ...

CROSSREFS

Cf. A277444 (colorings of Möbius ladders), A182406 (square grid graphs).

Columns k=1,2 are A000004 and A091940.

Rows n=1,2 are A000004 and A010673.

Sequence in context: A136615 A283950 A342376 * A209401 A029696 A118887

Adjacent sequences:  A277440 A277441 A277442 * A277444 A277445 A277446

KEYWORD

nonn,tabl

AUTHOR

Jeremy Tan, Oct 15 2016

STATUS

approved

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Last modified September 27 14:46 EDT 2022. Contains 357062 sequences. (Running on oeis4.)