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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 (list; graph; refs; listen; history; text; internal format)
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

R. H. Hardin, Table of n, a(n) for n = 1..210

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

Adjacent sequences:  A211488 A211489 A211490 * A211492 A211493 A211494

KEYWORD

nonn

AUTHOR

R. H. Hardin, Apr 13 2012

STATUS

approved

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Last modified May 17 00:26 EDT 2022. Contains 353724 sequences. (Running on oeis4.)