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A318244 a(n) is the number of configurations of n indistinguishable pairs placed on the vertices of the ladder graph P_2 X P_n such that only one such pair is joined by an edge. 7
1, 0, 8, 34, 347, 3666, 47484, 707480, 11971341, 226599568, 4744010444, 108834109034, 2714992695407, 73169624071138, 2118530753728184, 65582753432993648, 2161565971116312537, 75572040870327124064, 2793429487732659591888, 108847840347732886117874, 4459207771645802095292995 (list; graph; refs; listen; history; text; internal format)



This is a companion entry to A318243 and uses an inclusion-exclusion method on the matching numbers given there.

This is also the number of "1-domino" configurations in the game of memory played on a 2 X n rectangular array, see [Young]. - Donovan Young, Oct 23 2018


Table of n, a(n) for n=1..21.

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.


a(n) = Sum_{k=0..n-1} (-1)^k*(2*n-2*k-3)!! * A318243(n,k) where and 0!! = (-1)!! = 1; proved by inclusion-exclusion.


For the case n = 2, if one pair is joined by an edge, then the remaining pair is forced to be joined by the remaining edge. Thus a(2) = 0.


Cf. A046741, A318243, A318267, A318268, A318269, A318270. When no pair is joined by an edge, the number of configurations is given by A265167.

Sequence in context: A223015 A222796 A203445 * A280395 A158991 A265161

Adjacent sequences:  A318241 A318242 A318243 * A318245 A318246 A318247




Donovan Young, Aug 22 2018



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Last modified September 20 06:51 EDT 2020. Contains 337264 sequences. (Running on oeis4.)