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A211329 Number of (n+1) X (n+1) -5..5 symmetric matrices with every 2 X 2 subblock having sum zero and one or two distinct values. 1
15, 19, 25, 35, 51, 77, 119, 187, 297, 475, 763, 1229, 1983, 3203, 5177, 8371, 13539, 21901, 35431, 57323, 92745, 150059, 242795, 392845, 635631, 1028467, 1664089, 2692547, 4356627, 7049165, 11405783, 18454939, 29860713, 48315643, 78176347 (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*(15 - 11*x - 13*x^2) / ((1 - x)*(1 - x - x^2)). - Colin Barker, Jul 17 2018

EXAMPLE

Some solutions for n=3:

.-1..1.-1.-1....4.-4..4.-4....1..1..1.-1....1.-1..1..1...-2..2.-2..2

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

.-1..1.-1.-1....4.-4..4.-4....1..1..1.-1....1.-1..1..1...-2..2.-2..2

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

CROSSREFS

Sequence in context: A257020 A234849 A164564 * A104298 A032475 A169728

Adjacent sequences:  A211326 A211327 A211328 * A211330 A211331 A211332

KEYWORD

nonn

AUTHOR

R. H. Hardin, Apr 07 2012

STATUS

approved

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Last modified October 19 16:17 EDT 2019. Contains 328223 sequences. (Running on oeis4.)