A211326 - OEIS

%I #8 Jul 16 2018 09:42:35

%S 25,63,149,357,829,1941,4479,10413,24087,56079,130523,305431,715961,

%T 1685595,3977689,9418701,22352933,53188057,126803131,302898825,

%U 724648975,1736139523,4164319291,9999028263,24029343133,57789827919,139068433021

%N Number of (n+1) X (n+1) -3..3 symmetric matrices with every 2 X 2 subblock having sum zero and one, two or three distinct values.

%C 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).

%H R. H. Hardin, <a href="/A211326/b211326.txt">Table of n, a(n) for n = 1..203</a>

%F Empirical: a(n) = 5*a(n-1) - a(n-2) - 29*a(n-3) + 33*a(n-4) + 50*a(n-5) - 88*a(n-6) - 14*a(n-7) + 73*a(n-8) - 22*a(n-9) - 10*a(n-10) + 4*a(n-11).

%F Empirical g.f.: x*(25 - 62*x - 141*x^2 + 400*x^3 + 195*x^4 - 855*x^5 + 89*x^6 + 663*x^7 - 248*x^8 - 102*x^9 + 44*x^10) / ((1 - x)*(1 - 2*x)*(1 + x - x^2)*(1 - 2*x - x^2)*(1 - 2*x^2)*(1 - x - 2*x^2 + x^3)). - _Colin Barker_, Jul 16 2018

%e Some solutions for n=3:

%e ..3.-3..0..0...-1..1..0..1...-1..1.-1..1....2..0..2.-1....0..0..0..1

%e .-3..3..0..0....1.-1..0.-1....1.-1..1.-1....0.-2..0.-1....0..0..0.-1

%e ..0..0.-3..3....0..0..1..0...-1..1.-1..1....2..0..2.-1....0..0..0..1

%e ..0..0..3.-3....1.-1..0.-1....1.-1..1.-1...-1.-1.-1..0....1.-1..1.-2

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 07 2012