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A211497 Number of (n+1)X(n+1) -4..4 symmetric matrices with every 2X2 subblock having sum zero and two, three or four distinct values 1

%I

%S 40,180,808,3636,16396,74104,335660,1523420,6925768,31527492,

%T 143656108,654965928,2986993420,13622286844,62110476152,283072002980,

%U 1289383564204,5869109209272,26695147549612,121321864635996,550906942638568

%N Number of (n+1)X(n+1) -4..4 symmetric matrices with every 2X2 subblock having sum zero and two, three or four distinct values

%C Symmetry and 2X2 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="/A211497/b211497.txt">Table of n, a(n) for n = 1..162</a>

%F Empirical: a(n) = 21*a(n-1) -177*a(n-2) +742*a(n-3) -1477*a(n-4) +665*a(n-5) +1725*a(n-6) -952*a(n-7) -1462*a(n-8) -476*a(n-9) -48*a(n-10)

%e Some solutions for n=3

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_ Apr 13 2012

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Last modified July 2 21:48 EDT 2022. Contains 355029 sequences. (Running on oeis4.)