A243510 Number of ways the maximal number of domicules can be placed on an n X n square.

1, 1, 3, 58, 280, 170985, 3037561, 35203565096, 3263262629905, 580992839261272720, 326207195516663381931, 811740344447523575023878026, 3011882198082438957330143630563, 98662906581850761030365769529236858241, 2565014347691062208319404612723752103028288

Offset: 0

Author

Alois P. Heinz, Jun 05 2014

Keywords

• nonn

Comments

Number of maximum matchings in the n X n king graph. - Eric W. Weisstein, Jun 20 2017

Examples

			a(2) = 3:
  +---+  +---+  +---+
  |o-o|  |o o|  |o o|
  |   |  || ||  | X |
  |o-o|  |o o|  |o o|
  +---+  +---+  +---+.
a(3) = 58:
  +-----+  +-----+  +-----+
  |o-o o|  |o o o|  |o o-o|
  |    ||  | X  ||  | \   |
  |o   o|  |o o o|  |o o o|
  ||    |  |     |  ||  / |
  |o o-o|  |o-o  |  |o o  |
  +-----+  +-----+  +-----+  ... .
		

Links

• Eric Weisstein's World of Mathematics, Independent Edge Set
• Eric Weisstein's World of Mathematics, King Graph
• Eric Weisstein's World of Mathematics, Matching
• Eric Weisstein's World of Mathematics, Maximum Independent Edge Set
• Wikipedia, King's graph

Crossrefs

Cf. A243511.

Even bisection gives A239273.

Formula

a(n) = A243424(n,floor(n^2/2)).