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A211466 Number of (n+1) X (n+1) -8..8 symmetric matrices with every 2 X 2 subblock having sum zero and one or two distinct values. 1

%I

%S 25,33,45,65,97,149,233,369,589,945,1521,2453,3961,6401,10349,16737,

%T 27073,43797,70857,114641,185485,300113,485585,785685,1271257,2056929,

%U 3328173,5385089,8713249,14098325,22811561,36909873,59721421,96631281

%N Number of (n+1) X (n+1) -8..8 symmetric matrices with every 2 X 2 subblock having sum zero and one or two 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="/A211466/b211466.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) - a(n-3).

%F Empirical g.f.: x*(25 - 17*x - 21*x^2) / ((1 - x)*(1 - x - x^2)). - _Colin Barker_, Jul 18 2018

%e Some solutions for n=3:

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

%e ..1..1.-1.-1....5.-5..5.-5....3.-3..3.-3....2.-6..2.-6...-2..6.-2..6

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

%e ..3.-1..1.-3....5.-5..5.-5....3.-3..3.-3....2.-6..2.-6...-2..6.-2..6

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 12 2012

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Last modified November 22 13:47 EST 2019. Contains 329393 sequences. (Running on oeis4.)