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A211328 Number of (n+1) X (n+1) -3..3 symmetric matrices with every 2 X 2 subblock having sum zero and two, three or four distinct values. 1

%I

%S 24,86,310,1134,4190,15582,58130,217014,809418,3013130,11188738,

%T 41433570,153004862,563461506,2069583806,7582810302,27719202126,

%U 101113824446,368123385634,1337824919574,4853929237946,17584750606794,63618436617746

%N Number of (n+1) X (n+1) -3..3 symmetric matrices with every 2 X 2 subblock having sum zero and two, three or four 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="/A211328/b211328.txt">Table of n, a(n) for n = 1..90</a>

%F Empirical: a(n) = 13*a(n-1) - 63*a(n-2) + 130*a(n-3) - 65*a(n-4) - 115*a(n-5) + 69*a(n-6) + 68*a(n-7) + 12*a(n-8).

%F Empirical g.f.: 2*x*(12 - 113*x + 352*x^2 - 299*x^3 - 321*x^4 + 302*x^5 + 249*x^6 + 42*x^7) / ((1 - 2*x)*(1 - 3*x)*(1 - 2*x - x^2)*(1 - 3*x - x^2)*(1 - 3*x - 2*x^2)). - _Colin Barker_, Jul 17 2018

%e Some solutions for n=3:

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

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

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

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

%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.)