A211331 Number of (n+1) X (n+1) -5..5 symmetric matrices with every 2 X 2 subblock having sum zero and one or three distinct values.

47, 99, 201, 397, 789, 1531, 2999, 5801, 11307, 21927, 42763, 83311, 162977, 319089, 626611, 1232377, 2429037, 4795401, 9482053, 18776315, 37223555, 73884069, 146773655, 291853839, 580697115, 1156276783, 2303407301, 4591264605

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) + 4*a(n-2) - 32*a(n-3) + 8*a(n-4) + 95*a(n-5) - 60*a(n-6) - 130*a(n-7) + 101*a(n-8) + 81*a(n-9) - 64*a(n-10) - 18*a(n-11) + 12*a(n-12).

Empirical g.f.: x*(47 - 89*x - 383*x^2 + 701*x^3 + 1189*x^4 - 2038*x^5 - 1770*x^6 + 2708*x^7 + 1255*x^8 - 1596*x^9 - 340*x^10 + 296*x^11) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 - x - x^2)*(1 - 2*x^2)*(1 - 3*x^2)*(1 - x - 2*x^2 + x^3)). - Colin Barker, Jul 17 2018

Example

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

Crossrefs

Sequence in context: A176134 A155844 A245688 * A141961 A357746 A142661

Adjacent sequences: A211328 A211329 A211330 * A211332 A211333 A211334

Keyword

nonn

Author

R. H. Hardin, Apr 07 2012

Status

approved