A211333 - OEIS

%I #4 Apr 07 2012 19:40:22

%S 61,153,359,811,1825,4073,9117,20435,46019,104103,236721,541185,

%T 1243505,2872291,6664963,15538035,36366709,85451073,201438293,

%U 476368999,1129466571,2684618219,6394000481,15257754137,36465654269,87277538267

%N Number of (n+1)X(n+1) -5..5 symmetric matrices with every 2X2 subblock having sum zero and one, two or three distinct values

%C Symmetry and 2X2 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="/A211333/b211333.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) +10*a(n-2) -82*a(n-3) -10*a(n-4) +576*a(n-5) -286*a(n-6) -2266*a(n-7) +1807*a(n-8) +5476*a(n-9) -5310*a(n-10) -8379*a(n-11) +9038*a(n-12) +8059*a(n-13) -9334*a(n-14) -4671*a(n-15) +5778*a(n-16) +1496*a(n-17) -2024*a(n-18) -226*a(n-19) +356*a(n-20) +12*a(n-21) -24*a(n-22)

%e Some solutions for n=3

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

%e ..1.-2..1.-1....2.-4..1.-4....1.-4..1.-4....1..0.-2..0....1..1..1..1

%e ..0..1..0..0....1..1..2..1....2..1..2..1....1.-2..4.-2...-3..1.-3..1

%e ..0.-1..0..0....2.-4..1.-4....1.-4..1.-4....1..0.-2..0....1..1..1..1

%K nonn

%O 1,1

%A _R. H. Hardin_ Apr 07 2012