

A265167


Number of n X 2 arrays containing 2 copies of 0..n1 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
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OFFSET

1,3


COMMENTS

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 "0domino" configurations in the game of memory played on a 2 X n rectangular array, see [Young].  Donovan Young, Oct 22 2018


LINKS



FORMULA

a(n) = Sum_{k=0..n} (1)^k*(2*n2*k1)!! * A046741(n,k) where and 0!! = (1)!! = 1; proved by inclusionexclusion, 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



KEYWORD

nonn


AUTHOR



STATUS

approved



