A265167 Number of n X 2 arrays containing 2 copies of 0..n-1 with no equal horizontal or vertical neighbors and new values introduced sequentially from 0.

0, 1, 2, 21, 186, 2113, 27856, 422481, 7241480, 138478561, 2923183474, 67520866405, 1694065383154, 45878853274945, 1333966056696224, 41446945223914337, 1370476678395567376, 48051281596087884289

Offset: 1

Author

R. H. Hardin, Dec 03 2015

Keywords

• nonn

Comments

Column 2 of A265170.

a(n) is also the number of configurations of n indistinguishable pairs placed on the vertices of the ladder graph P_2 X P_n such that no such pair is joined by an edge; equivalently this is the number of "0-domino" configurations in the game of memory played on a 2 X n rectangular array, see [Young]. - Donovan Young, Oct 22 2018

Examples

			Some solutions for n=4
..0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1
..2..3....2..3....2..3....2..0....2..3....2..3....2..3....2..3....2..3....2..3
..0..1....3..2....0..2....1..3....0..1....3..0....3..1....1..2....3..2....0..2
..2..3....1..0....3..1....3..2....3..2....2..1....0..2....0..3....0..1....1..3
		

Links

• D. Young, The Number of Domino Matchings in the Game of Memory, Journal of Integer Sequences, Vol. 21 (2018), Article 18.8.1.
• Donovan Young, Generating Functions for Domino Matchings in the 2 * k Game of Memory, arXiv:1905.13165 [math.CO], 2019. Also in J. Int. Seq., Vol. 22 (2019), Article 19.8.7.

Crossrefs

Cf. A265170, A046741.

Formula

a(n) = Sum_{k=0..n} (-1)^k*(2*n-2*k-1)!! * A046741(n,k) where and 0!! = (-1)!! = 1; proved by inclusion-exclusion, see [Young].