A211254 Number of (n+1) X (n+1) -6..6 symmetric matrices with every 2 X 2 subblock having sum zero and three distinct values.

64, 130, 246, 456, 840, 1538, 2830, 5214, 9672, 18020, 33790, 63702, 120752, 230126, 440512, 847370, 1635656, 3170660, 6162524, 12020244, 23492880, 46050762, 90403706, 177902814, 350479066, 691826684, 1366757298, 2704492222, 5354853154

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) = 5*a(n-1) - 36*a(n-3) + 41*a(n-4) + 82*a(n-5) - 151*a(n-6) - 54*a(n-7) + 204*a(n-8) - 28*a(n-9) - 110*a(n-10) + 36*a(n-11) + 20*a(n-12) - 8*a(n-13).

Empirical g.f.: 2*x*(32 - 95*x - 202*x^2 + 765*x^3 + 308*x^4 - 2192*x^5 + 237*x^6 + 2761*x^7 - 876*x^8 - 1493*x^9 + 604*x^10 + 284*x^11 - 124*x^12) / ((1 - x)*(1 - 2*x)*(1 - x - x^2)*(1 - 2*x^2)*(1 - x - 2*x^2 + x^3)*(1 - 4*x^2 + 2*x^4)). - Colin Barker, Jul 16 2018

Example

Some solutions for n=3:
.-3..4.-3..4....6.-1..6.-1...-5..1.-5..3....6..0..6.-3....4..1..1..1
..4.-5..4.-5...-1.-4.-1.-4....1..3..1..1....0.-6..0.-3....1.-6..4.-6
.-3..4.-3..4....6.-1..6.-1...-5..1.-5..3....6..0..6.-3....1..4.-2..4
..4.-5..4.-5...-1.-4.-1.-4....3..1..3.-1...-3.-3.-3..0....1.-6..4.-6

Crossrefs

Sequence in context: A235058 A366287 A252088 * A252081 A068410 A250654

Adjacent sequences: A211251 A211252 A211253 * A211255 A211256 A211257

Keyword

nonn

Author

R. H. Hardin, Apr 06 2012

Status

approved