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A212195 Square array A(n,k), n>=1, k>=1, read by antidiagonals: A(n,k) is the number of n-colorings of the staggered hexagonal square grid graph SH_(k,k). 14
1, 0, 2, 0, 0, 3, 0, 0, 6, 4, 0, 0, 6, 48, 5, 0, 0, 6, 1056, 180, 6, 0, 0, 6, 45696, 32940, 480, 7, 0, 0, 6, 4038432, 30847500, 393600, 1050, 8, 0, 0, 6, 743601024, 148046704020, 3312560640, 2735250, 2016, 9 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

The staggered hexagonal square grid graph SH_(n,n) has n^2 = A000290(n) vertices and (n-1)*(3*n-1) = A045944(n-1) edges; see A212194 for example. The chromatic polynomial of SH_(n,n) has n^2+1 = A002522(n) coefficients.

A differs from A212163 first at (n,k) = (4,5): A(4,5) = 4038432, A212163(4,5) = 4034304.

LINKS

Table of n, a(n) for n=1..45.

Wikipedia, Chromatic Polynomial

EXAMPLE

Square array A(n,k) begins:

  1,    0,       0,            0,                 0, ...

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

  3,    6,       6,            6,                 6, ...

  4,   48,    1056,        45696,           4038432, ...

  5,  180,   32940,     30847500,      148046704020, ...

  6,  480,  393600,   3312560640,   286170443437440, ...

  7, 1050, 2735250, 123791435250, 97337320223288250, ...

CROSSREFS

Columns k=1-6 give: A000027, A047927(n) = 6*A002417(n-2), 6*A068244, 6*A068245, 6*A068248, 6*A068249.

Rows n=1-10, 16-18 give: A000007, A000038, A040006, 4*A068283, 5*A068284, 6*A068285, 7*A068286, 8*A068287, 9*A068288, 10*A068289, 16*A068290, 17*A068291, 18*A068292.

Cf. A212163, A212194.

Sequence in context: A114699 A182797 A212163 * A228926 A321414 A268865

Adjacent sequences:  A212192 A212193 A212194 * A212196 A212197 A212198

KEYWORD

nonn,tabl

AUTHOR

Alois P. Heinz, May 03 2012

STATUS

approved

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Last modified April 23 06:38 EDT 2021. Contains 343201 sequences. (Running on oeis4.)