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A211495 Number of (n+1) X (n+1) -4..4 symmetric matrices with every 2 X 2 subblock having sum zero and three or four distinct values. 1
28, 96, 336, 1208, 4360, 15792, 57128, 206424, 744656, 2682848, 9656216, 34733096, 124894432, 449073872, 1614961224, 5809590552, 20908485840, 75288818816, 271266031480, 977986031752, 3528175174080, 12736476508848, 46007333388584 (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) = 7*a(n-1) - a(n-2) - 75*a(n-3) + 78*a(n-4) + 268*a(n-5) - 296*a(n-6) - 316*a(n-7) + 272*a(n-8) - 48*a(n-9).

Empirical g.f.: 4*x*(7 - 25*x - 77*x^2 + 263*x^3 + 314*x^4 - 828*x^5 - 526*x^6 + 578*x^7 - 108*x^8) / ((1 - 2*x)*(1 - 2*x - 6*x^2)*(1 - x - 6*x^2 + 2*x^3)*(1 - 2*x - 5*x^2 + 2*x^3)). - Colin Barker, Jul 18 2018

EXAMPLE

Some solutions for n=3:

.-2..3.-2..3....4..0..4.-2...-3..2.-3..0...-2..1.-3..2...-4..3..0..3

..3.-4..3.-4....0.-4..0.-2....2.-1..2..1....1..0..2.-1....3.-2.-1.-2

.-2..3.-2..3....4..0..4.-2...-3..2.-3..0...-3..2.-4..3....0.-1..4.-1

..3.-4..3.-4...-2.-2.-2..0....0..1..0..3....2.-1..3.-2....3.-2.-1.-2

CROSSREFS

Sequence in context: A005971 A189808 A130085 * A233374 A231230 A233375

Adjacent sequences:  A211492 A211493 A211494 * A211496 A211497 A211498

KEYWORD

nonn

AUTHOR

R. H. Hardin, Apr 13 2012

STATUS

approved

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Last modified May 20 23:05 EDT 2022. Contains 353886 sequences. (Running on oeis4.)