A089980 Array read by antidiagonals: T(n,m) = number of independent sets in the grid graph P_n X P_m.

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 5, 7, 5, 1, 1, 8, 17, 17, 8, 1, 1, 13, 41, 63, 41, 13, 1, 1, 21, 99, 227, 227, 99, 21, 1, 1, 34, 239, 827, 1234, 827, 239, 34, 1, 1, 55, 577, 2999, 6743, 6743, 2999, 577, 55, 1, 1, 89, 1393, 10897, 36787, 55447, 36787, 10897, 1393, 89, 1

Offset: 0

Author

Mitch Harris, Nov 17 2003

Keywords

• nonn
• tabl

Comments

This table is indexed starting at 0. The table in A089934 is 1 based.

A181031 is essentially the same array (see the Comments by Steve Butler in A006506). - N. J. A. Sloane, Jan 27 2015

Examples

			Square array T(n,m) begins:
  1,  1,  1,   1,    1,     1, ...
  1,  2,  3,   5,    8,    13, ...
  1,  3,  7,  17,   41,    99, ...
  1,  5, 17,  63,  227,   827, ...
  1,  8, 41, 227, 1234,  6743, ...
  1, 13, 99, 827, 6743, 55447, ...
		

Links

• Liang Kai, Antidiagonals n = 0..78, flattened
• Kai Liang, Independent Set Enumeration in King Graphs by Tensor Network Contractions, arXiv:2505.12776 [math.CO], 2025. See p. 1.
• Kai Liang, Independent Set Enumeration and Estimation of Related Constants of Grid Graphs, arXiv:2507.04007 [math.CO], 2025. See p. 1.

Crossrefs

Main entry: A089934.

Main diagonal gives A006506.

Cf. A181031.