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A211323 Number of (n+1) X (n+1) -3..3 symmetric matrices with every 2 X 2 subblock having sum zero and three distinct values. 1

%I

%S 14,24,42,76,140,262,496,948,1826,3540,6900,13510,26552,52348,103474,

%T 204972,406748,808326,1608288,3203044,6384194,12732964,25408612,

%U 50724486,101298920,202355052,404317266,807998908,1614969356,3228274630

%N Number of (n+1) X (n+1) -3..3 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="/A211323/b211323.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) - 4*a(n-2) - a(n-3) + 2*a(n-4).

%F Empirical g.f.: 2*x*(7 - 16*x + x^2 + 9*x^3) / ((1 - x)*(1 - 2*x)*(1 - x - x^2)). - _Colin Barker_, Jul 16 2018

%e Some solutions for n=3.

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 07 2012

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Last modified October 28 17:59 EDT 2021. Contains 348329 sequences. (Running on oeis4.)