A211813 - OEIS

A211813

Number of (n+1) X (n+1) -10..10 symmetric matrices with every 2 X 2 subblock having sum zero and two distinct values.

32, 44, 62, 92, 140, 218, 344, 548, 878, 1412, 2276, 3674, 5936, 9596, 15518, 25100, 40604, 65690, 106280, 171956, 278222, 450164, 728372, 1178522, 1906880, 3085388, 4992254, 8077628, 13069868, 21147482, 34217336, 55364804, 89582126, 144946916

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OFFSET

1,1

COMMENTS

Symmetry and 2 X 2 block sums zero implies that the diagonal x(i,i) are equal modulo 2 and x(i,j) = (x(i,i)+x(j,j))/2*(-1)^(i-j).

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..175

FORMULA

Empirical: a(n) = 2*a(n-1) - a(n-3).

Empirical g.f.: 2*x*(16 - 10*x - 13*x^2) / ((1 - x)*(1 - x - x^2)). - Colin Barker, Jul 20 2018

EXAMPLE

Some solutions for n=3:

.-1..1.-1..1...-9..3.-3..3....3.-1..1.-3...-7..7.-7..7....1.-1.-1.-1

..1.-1..1.-1....3..3.-3..3...-1.-1..1..1....7.-7..7.-7...-1..1..1..1

.-1..1.-1..1...-3.-3..3.-3....1..1.-1.-1...-7..7.-7..7...-1..1.-3..1

..1.-1..1.-1....3..3.-3..3...-3..1.-1..3....7.-7..7.-7...-1..1..1..1

CROSSREFS

Sequence in context: A035112 A308765 A236324 * A353234 A303959 A304602

Adjacent sequences: A211810 A211811 A211812 * A211814 A211815 A211816

KEYWORD

nonn

AUTHOR

R. H. Hardin, Apr 21 2012

STATUS

approved