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 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. 3
 0, 1, 2, 21, 186, 2113, 27856, 422481, 7241480, 138478561, 2923183474, 67520866405, 1694065383154, 45878853274945, 1333966056696224, 41446945223914337, 1370476678395567376, 48051281596087884289 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 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 LINKS Table of n, a(n) for n=1..18. 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. 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]. EXAMPLE 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 CROSSREFS Cf. A265170, A046741. Sequence in context: A112673 A263435 A202028 * A037749 A037630 A037756 Adjacent sequences: A265164 A265165 A265166 * A265168 A265169 A265170 KEYWORD nonn AUTHOR R. H. Hardin, Dec 03 2015 STATUS approved

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Last modified August 11 21:40 EDT 2024. Contains 375073 sequences. (Running on oeis4.)