A137308 Number of dimer coverings on n X n square if n is even; number of dimer arrangements with exactly one monomer if n is odd.

1, 1, 2, 18, 36, 2180, 6728, 2200776, 12988816, 20355006224, 258584046368, 1801272981919008, 53060477521960000, 1560858753560238398528, 112202208776036178000000, 13428038397958481723104394368

Offset: 0

Author

Steven Finch, Apr 03 2008

Keywords

• nonn

Comments

Subsequence of even-subscripted terms is A004003.

Rightmost diagonal of A242861.

Also the number of maximum matchings in the n X n grid graph. - Eric W. Weisstein, May 28 2017

References

• Y. Kong, Packing dimers on (2p+1) X (2q+1) lattices, Phys. Rev. E 73 (2006) 016106

Links

• Steven Finch, Table of n, a(n) for n = 0..19
• Eric Weisstein's World of Mathematics, Grid Graph
• Eric Weisstein's World of Mathematics, Matching
• Eric Weisstein's World of Mathematics, Maximum Independent Edge Set

Crossrefs

Cf. A004003, A242861.

Extensions

a(0)=1 prepended by Alois P. Heinz, Aug 15 2021