

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
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OFFSET

1,3


COMMENTS

This is a companion entry to A318243 and uses an inclusionexclusion method on the matching numbers given there.
This is also the number of "1domino" configurations in the game of memory played on a 2 X n rectangular array, see [Young].  Donovan Young, Oct 23 2018


LINKS

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.


FORMULA

a(n) = Sum_{k=0..n1} (1)^k*(2*n2*k3)!! * A318243(n,k) where and 0!! = (1)!! = 1; proved by inclusionexclusion.


EXAMPLE

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.


CROSSREFS

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


KEYWORD

nonn


AUTHOR

Donovan Young, Aug 22 2018


STATUS

approved



