A156431 Number of n X n arrays of squares of integers, symmetric under 90-degree rotation, with all rows summing to 2.

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

Robert Israel, Table of n, a(n) for n = 2..807

Robert Israel, Proof of recurrence

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

Adjacent sequences: A156428 A156429 A156430 * A156432 A156433 A156434

Keyword

nonn

Author

R. H. Hardin, Feb 09 2009

Status

approved