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A211116 Number of (n+1) X (n+1) -2..2 symmetric matrices with every 2 X 2 subblock having sum zero and one, two or three distinct values. 1

%I #8 Jul 16 2018 04:47:24

%S 13,31,75,177,415,963,2227,5137,11855,27397,63483,147557,344175,

%T 805635,1892433,4460137,10544415,24999069,59419405,141550383,

%U 337872559,807871799,1934541399,4638401749,11133523165,26748531157,64314484855

%N Number of (n+1) X (n+1) -2..2 symmetric matrices with every 2 X 2 subblock having sum zero and one, 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="/A211116/b211116.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 7*a(n-1) - 15*a(n-2) + a(n-3) + 33*a(n-4) - 28*a(n-5) - 12*a(n-6) + 16*a(n-7) + a(n-8) - 2*a(n-9).

%F Empirical g.f.: x*(13 - 60*x + 53*x^2 + 104*x^3 - 159*x^4 - 21*x^5 + 83*x^6 + x^7 - 10*x^8) / ((1 - x)*(1 - 2*x)*(1 - x - x^2)*(1 - 2*x - x^2)*(1 - x - 2*x^2 + x^3)). - _Colin Barker_, Jul 16 2018

%e Some solutions for n=3:

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 02 2012

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Last modified March 29 04:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)