A211491 Number of (n+1) X (n+1) -4..4 symmetric matrices with every 2 X 2 subblock having sum zero and three distinct values.

28, 56, 110, 206, 392, 728, 1372, 2562, 4838, 9126, 17360, 33116, 63572, 122558, 237382, 461802, 901448, 1766496, 3470060, 6838226, 13498502, 26712038, 52921792, 105046092, 208674308, 415112766, 826217510, 1646150186, 3280944632

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..210

Formula

Empirical: a(n) = 4*a(n-1) + a(n-2) - 21*a(n-3) + 16*a(n-4) + 29*a(n-5) - 34*a(n-6) - 6*a(n-7) + 12*a(n-8).

Empirical g.f.: 2*x*(14 - 28*x - 71*x^2 + 149*x^3 + 93*x^4 - 222*x^5 - 19*x^6 + 82*x^7) / ((1 - x)*(1 - 2*x)*(1 - x - x^2)*(1 - 2*x^2)*(1 - 3*x^2)). - Colin Barker, Jul 18 2018

Example

Some solutions for n=3:
..4.-2..1.-2...-2..3.-2..3...-2..1..0.-1....4.-1..4.-1....0.-1..0.-1
.-2..0..1..0....3.-4..3.-4....1..0.-1..2...-1.-2.-1.-2...-1..2.-1..2
..1..1.-2..1...-2..3.-2..3....0.-1..2.-3....4.-1..4.-1....0.-1..0.-1
.-2..0..1..0....3.-4..3.-4...-1..2.-3..4...-1.-2.-1.-2...-1..2.-1..2

Crossrefs

Sequence in context: A040756 A135628 A204646 * A270297 A068576 A272185

Adjacent sequences: A211488 A211489 A211490 * A211492 A211493 A211494

Keyword

nonn

Author

R. H. Hardin, Apr 13 2012

Status

approved