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A211466 Number of (n+1) X (n+1) -8..8 symmetric matrices with every 2 X 2 subblock having sum zero and one or two distinct values. 1
25, 33, 45, 65, 97, 149, 233, 369, 589, 945, 1521, 2453, 3961, 6401, 10349, 16737, 27073, 43797, 70857, 114641, 185485, 300113, 485585, 785685, 1271257, 2056929, 3328173, 5385089, 8713249, 14098325, 22811561, 36909873, 59721421, 96631281 (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) = 2*a(n-1) - a(n-3).

Empirical g.f.: x*(25 - 17*x - 21*x^2) / ((1 - x)*(1 - x - x^2)). - Colin Barker, Jul 18 2018

EXAMPLE

Some solutions for n=3:

.-3..1.-1..3...-5..5.-5..5...-3..3.-3..3....2..2..2..2...-2.-2.-2.-2

..1..1.-1.-1....5.-5..5.-5....3.-3..3.-3....2.-6..2.-6...-2..6.-2..6

.-1.-1..1..1...-5..5.-5..5...-3..3.-3..3....2..2..2..2...-2.-2.-2.-2

..3.-1..1.-3....5.-5..5.-5....3.-3..3.-3....2.-6..2.-6...-2..6.-2..6

CROSSREFS

Sequence in context: A219951 A209333 A131610 * A269345 A134099 A129074

Adjacent sequences:  A211463 A211464 A211465 * A211467 A211468 A211469

KEYWORD

nonn

AUTHOR

R. H. Hardin, Apr 12 2012

STATUS

approved

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Last modified February 23 02:29 EST 2019. Contains 320411 sequences. (Running on oeis4.)