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A211326 Number of (n+1) X (n+1) -3..3 symmetric matrices with every 2 X 2 subblock having sum zero and one, two or three distinct values. 1
25, 63, 149, 357, 829, 1941, 4479, 10413, 24087, 56079, 130523, 305431, 715961, 1685595, 3977689, 9418701, 22352933, 53188057, 126803131, 302898825, 724648975, 1736139523, 4164319291, 9999028263, 24029343133, 57789827919, 139068433021 (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..203

FORMULA

Empirical: a(n) = 5*a(n-1) - a(n-2) - 29*a(n-3) + 33*a(n-4) + 50*a(n-5) - 88*a(n-6) - 14*a(n-7) + 73*a(n-8) - 22*a(n-9) - 10*a(n-10) + 4*a(n-11).

Empirical g.f.: x*(25 - 62*x - 141*x^2 + 400*x^3 + 195*x^4 - 855*x^5 + 89*x^6 + 663*x^7 - 248*x^8 - 102*x^9 + 44*x^10) / ((1 - x)*(1 - 2*x)*(1 + x - x^2)*(1 - 2*x - x^2)*(1 - 2*x^2)*(1 - x - 2*x^2 + x^3)). - Colin Barker, Jul 16 2018

EXAMPLE

Some solutions for n=3:

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

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

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

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

CROSSREFS

Sequence in context: A166873 A242317 A251688 * A103645 A061970 A159008

Adjacent sequences:  A211323 A211324 A211325 * A211327 A211328 A211329

KEYWORD

nonn

AUTHOR

R. H. Hardin, Apr 07 2012

STATUS

approved

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Last modified August 20 18:11 EDT 2019. Contains 326154 sequences. (Running on oeis4.)