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A211331 Number of (n+1) X (n+1) -5..5 symmetric matrices with every 2 X 2 subblock having sum zero and one or three distinct values. 1

%I

%S 47,99,201,397,789,1531,2999,5801,11307,21927,42763,83311,162977,

%T 319089,626611,1232377,2429037,4795401,9482053,18776315,37223555,

%U 73884069,146773655,291853839,580697115,1156276783,2303407301,4591264605

%N Number of (n+1) X (n+1) -5..5 symmetric matrices with every 2 X 2 subblock having sum zero and one 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="/A211331/b211331.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) + 4*a(n-2) - 32*a(n-3) + 8*a(n-4) + 95*a(n-5) - 60*a(n-6) - 130*a(n-7) + 101*a(n-8) + 81*a(n-9) - 64*a(n-10) - 18*a(n-11) + 12*a(n-12).

%F Empirical g.f.: x*(47 - 89*x - 383*x^2 + 701*x^3 + 1189*x^4 - 2038*x^5 - 1770*x^6 + 2708*x^7 + 1255*x^8 - 1596*x^9 - 340*x^10 + 296*x^11) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 - x - x^2)*(1 - 2*x^2)*(1 - 3*x^2)*(1 - x - 2*x^2 + x^3)). - _Colin Barker_, Jul 17 2018

%e Some solutions for n=3:

%e .-5..4.-3..4....0.-1.-1..0...-3..2.-1..2....0..0..0..2....3.-2..3..1

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

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

%e ..4.-3..2.-3....0..1..1..0....2.-1..0.-1....2.-2..2.-4....1.-2..1.-5

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 07 2012

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Last modified October 14 05:08 EDT 2019. Contains 327995 sequences. (Running on oeis4.)