A068245 -id:A068245 - cp's OEIS frontend

A212163 Square array A(n,k), n>=1, k>=1, read by antidiagonals: A(n,k) is the number of n-colorings of the rhombic hexagonal square grid graph RH_(k,k).

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, 4034304, 30847500, 393600, 1050, 8, 0, 0, 6, 739642368, 148039757460, 3312560640, 2735250, 2016, 9

Offset: 1

Alois P. Heinz, May 02 2012

The rhombic hexagonal square grid graph RH_(n,n) has n^2 = A000290(n) vertices and (n-1)*(3*n-1) = A045944(n-1) edges; see A212162 for example. The chromatic polynomial of RH_(n,n) has n^2+1 = A002522(n) coefficients.

A differs from A212195 first at (n,k) = (4,5): A(4,5) = 4034304, A212195(4,5) = 4038432.

			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,           4034304, ...
  5,  180,   32940,     30847500,      148039757460, ...
  6,  480,  393600,   3312560640,   286169360240640, ...
  7, 1050, 2735250, 123791435250, 97337270132408250, ...

Andrew Howroyd, Table of n, a(n) for n = 1..153
Wikipedia, Chromatic Polynomial

Columns k=1-6 give: A000027, A047927(n) = 6*A002417(n-2), 6*A068244, 6*A068245, 6*A068246, 6*A068247.
Rows n=1-15 give: A000007, A000038, A040006, 4*A068271, 5*A068272, 6*A068273, 7*A068274, 8*A068275, 9*A068276, 10*A068277, 11*A068278, 12*A068279, 13*A068280, 14*A068281, 15*A068282.
Cf. A212162, A212195, A208054, A208050.

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).

Original entry on oeis.org

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

Offset: 1

Alois P. Heinz, May 03 2012

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.

			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, ...

Wikipedia, Chromatic Polynomial

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.

cp's OEIS Frontend

A212163 Square array A(n,k), n>=1, k>=1, read by antidiagonals: A(n,k) is the number of n-colorings of the rhombic hexagonal square grid graph RH_(k,k).

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