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A156431
Number of n X n arrays of squares of integers, symmetric under 90-degree rotation, with all rows summing to 2.
1
1, 0, 2, 0, 12, 0, 90, 0, 810, 0, 8940, 0, 116760, 0, 1756860, 0, 29933820, 0, 569744280, 0, 11981526480, 0, 275893362360, 0, 6903968231160, 0, 186558764792400, 0, 5413973807642400
OFFSET
2,3
COMMENTS
a(2*n) is the number of n X n 0-1 matrices A such that all row sums of A + A^T equal 2. - Robert Israel, Feb 19 2019
LINKS
FORMULA
From Robert Israel, Feb 18 2019: (Start)
a(2k+1) = 0.
a(2k) = 2*(k-1)*(k-2)*a(2k-6) - (k-1)*a(2k-4) + (2k-1)*a(2k-2).
(End)
MAPLE
f:= gfun:-rectoproc({b(k) = 2*(k-1)*(k-2)*b(k-3)-(k-1)*b(k-2)+(2*k-1)*b(k-1), b(0)=1, b(1)=1, b(2)=2}, b(k), remember):
seq(op([f(k), 0]), k=0..50); # Robert Israel, Feb 18 2019
MATHEMATICA
a[n_] := a[n] = If[OddQ[n], 0, Switch[n, 2, 1, 4, 2, 6, 12, _, (n-4)*(n/2-1)*a[n-6] - (n/2-1)*a[n-4] + (n-1)*a[n-2]]];
Table[a[n], {n, 2, 40}] (* Jean-François Alcover, Aug 28 2022, after Robert Israel *)
CROSSREFS
Sequence in context: A167345 A292496 A285480 * A067994 A236219 A143246
KEYWORD
nonn
AUTHOR
R. H. Hardin, Feb 09 2009
STATUS
approved