A211330 - OEIS

%I #7 Jul 17 2018 08:39:37

%S 46,90,172,316,588,1070,1974,3608,6670,12310,22930,42818,80560,152240,

%T 289462,553112,1062084,2049116,3968676,7718410,15055782,29469492,

%U 57813502,113731682,224119946,442604110,875210760,1733534748,3436966638

%N Number of (n+1) X (n+1) -5..5 symmetric matrices with every 2 X 2 subblock having sum zero and 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="/A211330/b211330.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) - a(n-2) - 31*a(n-3) + 39*a(n-4) +  56*a(n-5) - 116*a(n-6) - 14*a(n-7) + 115*a(n-8) - 34*a(n-9) - 30*a(n-10) + 12*a(n-11).

%F Empirical g.f.: 2*x*(23 - 70*x - 116*x^2 + 486*x^3 + 88*x^4 - 1154*x^5 + 298*x^6 + 1082*x^7 - 466*x^8 - 309*x^9 + 142*x^10) / ((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

%e Some solutions for n=3.

%e .-1..2.-1..0...-5..2.-5..1...-1..2.-1..2....0.-1.-1.-1...-1..2..2..0

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

%e .-1..2.-1..0...-5..2.-5..1...-1..2.-1..2...-1..0.-2..0....2.-1..5.-3

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 07 2012