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A211325 Number of (n+1) X (n+1) -3..3 symmetric matrices with every 2 X 2 subblock having sum zero and two or three distinct values. 1

%I

%S 24,58,126,274,572,1202,2470,5118,10466,21560,44066,90582,185338,

%T 380818,780392,1604082,3292390,6772414,13921038,28660928,58993382,

%U 121571918,250540314,516800746,1066237980,2201452066,4546640338,9396025014

%N Number of (n+1) X (n+1) -3..3 symmetric matrices with every 2 X 2 subblock having sum zero and two or 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="/A211325/b211325.txt">Table of n, a(n) for n = 1..191</a>

%F Empirical: a(n) = 3*a(n-1) + 6*a(n-2) - 22*a(n-3) - 11*a(n-4) + 58*a(n-5) + 4*a(n-6) - 65*a(n-7) + 5*a(n-8) + 28*a(n-9) - 2*a(n-10) - 4*a(n-11).

%F Empirical g.f.: 2*x*(12 - 7*x - 96*x^2 + 38*x^3 + 267*x^4 - 70*x^5 - 307*x^6 + 57*x^7 + 141*x^8 - 14*x^9 - 22*x^10) / ((1 - 2*x)*(1 + x - x^2)*(1 - x - x^2)*(1 - 2*x^2)*(1 - x - 3*x^2 + x^3 + x^4)). - _Colin Barker_, Jul 16 2018

%e Some solutions for n=3:

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 07 2012

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Last modified October 20 19:42 EDT 2021. Contains 348118 sequences. (Running on oeis4.)