A211495 Number of (n+1) X (n+1) -4..4 symmetric matrices with every 2 X 2 subblock having sum zero and three or four distinct values.

28, 96, 336, 1208, 4360, 15792, 57128, 206424, 744656, 2682848, 9656216, 34733096, 124894432, 449073872, 1614961224, 5809590552, 20908485840, 75288818816, 271266031480, 977986031752, 3528175174080, 12736476508848, 46007333388584

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) = 7*a(n-1) - a(n-2) - 75*a(n-3) + 78*a(n-4) + 268*a(n-5) - 296*a(n-6) - 316*a(n-7) + 272*a(n-8) - 48*a(n-9).

Empirical g.f.: 4*x*(7 - 25*x - 77*x^2 + 263*x^3 + 314*x^4 - 828*x^5 - 526*x^6 + 578*x^7 - 108*x^8) / ((1 - 2*x)*(1 - 2*x - 6*x^2)*(1 - x - 6*x^2 + 2*x^3)*(1 - 2*x - 5*x^2 + 2*x^3)). - Colin Barker, Jul 18 2018

Example

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

Crossrefs

Sequence in context: A005971 A189808 A130085 * A233374 A231230 A233375

Adjacent sequences: A211492 A211493 A211494 * A211496 A211497 A211498

Keyword

nonn

Author

R. H. Hardin, Apr 13 2012

Status

approved