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A211491
Number of (n+1) X (n+1) -4..4 symmetric matrices with every 2 X 2 subblock having sum zero and three distinct values.
1
28, 56, 110, 206, 392, 728, 1372, 2562, 4838, 9126, 17360, 33116, 63572, 122558, 237382, 461802, 901448, 1766496, 3470060, 6838226, 13498502, 26712038, 52921792, 105046092, 208674308, 415112766, 826217510, 1646150186, 3280944632
OFFSET
1,1
COMMENTS
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).
LINKS
FORMULA
Empirical: a(n) = 4*a(n-1) + a(n-2) - 21*a(n-3) + 16*a(n-4) + 29*a(n-5) - 34*a(n-6) - 6*a(n-7) + 12*a(n-8).
Empirical g.f.: 2*x*(14 - 28*x - 71*x^2 + 149*x^3 + 93*x^4 - 222*x^5 - 19*x^6 + 82*x^7) / ((1 - x)*(1 - 2*x)*(1 - x - x^2)*(1 - 2*x^2)*(1 - 3*x^2)). - Colin Barker, Jul 18 2018
EXAMPLE
Some solutions for n=3:
..4.-2..1.-2...-2..3.-2..3...-2..1..0.-1....4.-1..4.-1....0.-1..0.-1
.-2..0..1..0....3.-4..3.-4....1..0.-1..2...-1.-2.-1.-2...-1..2.-1..2
..1..1.-2..1...-2..3.-2..3....0.-1..2.-3....4.-1..4.-1....0.-1..0.-1
.-2..0..1..0....3.-4..3.-4...-1..2.-3..4...-1.-2.-1.-2...-1..2.-1..2
CROSSREFS
Sequence in context: A040756 A135628 A204646 * A270297 A068576 A272185
KEYWORD
nonn
AUTHOR
R. H. Hardin, Apr 13 2012
STATUS
approved