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A211324 Number of (n+1) X (n+1) -3..3 symmetric matrices with every 2 X 2 subblock having sum zero and one or three distinct values. 1
15, 29, 55, 107, 209, 409, 805, 1583, 3127, 6175, 12233, 24241, 48141, 95655, 190343, 378967, 755249, 1505841, 3004341, 5996175, 11972503, 23911631, 47770041, 95451441, 190761021, 381287447, 762198439, 1523777639, 3046559585, 6091487857 (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) = 3*a(n-1) + 2*a(n-2) - 11*a(n-3) + a(n-4) + 12*a(n-5) - 2*a(n-6) - 4*a(n-7).

Empirical g.f.: x*(15 - 16*x - 62*x^2 + 49*x^3 + 82*x^4 - 36*x^5 - 36*x^6) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 - x - x^2)*(1 - 2*x^2)). - Colin Barker, Jul 16 2018

EXAMPLE

Some solutions for n=3:

.-1..0.-1..0....2..0..2.-1....0..0..1..0....0..0..0.-1...-2..0.-2..1

..0..1..0..1....0.-2..0.-1....0..0.-1..0....0..0..0..1....0..2..0..1

.-1..0.-1..0....2..0..2.-1....1.-1..2.-1....0..0..0.-1...-2..0.-2..1

..0..1..0..1...-1.-1.-1..0....0..0.-1..0...-1..1.-1..2....1..1..1..0

CROSSREFS

Sequence in context: A001356 A104811 A131877 * A146427 A202512 A014095

Adjacent sequences:  A211321 A211322 A211323 * A211325 A211326 A211327

KEYWORD

nonn

AUTHOR

R. H. Hardin, Apr 07 2012

STATUS

approved

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Last modified October 16 18:03 EDT 2019. Contains 328102 sequences. (Running on oeis4.)