A211325 - OEIS

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A211325

Number of (n+1) X (n+1) -3..3 symmetric matrices with every 2 X 2 subblock having sum zero and two or three distinct values.

24, 58, 126, 274, 572, 1202, 2470, 5118, 10466, 21560, 44066, 90582, 185338, 380818, 780392, 1604082, 3292390, 6772414, 13921038, 28660928, 58993382, 121571918, 250540314, 516800746, 1066237980, 2201452066, 4546640338, 9396025014

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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..191

FORMULA

Empirical: a(n) = 3*a(n-1) + 6*a(n-2) - 22*a(n-3) - 11*a(n-4) + 58*a(n-5) + 4*a(n-6) - 65*a(n-7) + 5*a(n-8) + 28*a(n-9) - 2*a(n-10) - 4*a(n-11).

Empirical g.f.: 2*x*(12 - 7*x - 96*x^2 + 38*x^3 + 267*x^4 - 70*x^5 - 307*x^6 + 57*x^7 + 141*x^8 - 14*x^9 - 22*x^10) / ((1 - 2*x)*(1 + x - x^2)*(1 - x - x^2)*(1 - 2*x^2)*(1 - x - 3*x^2 + x^3 + x^4)). - Colin Barker, Jul 16 2018

EXAMPLE

Some solutions for n=3:

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

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

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

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

CROSSREFS

Sequence in context: A232937 A190104 A255968 * A290303 A044126 A044507

Adjacent sequences: A211322 A211323 A211324 * A211326 A211327 A211328

KEYWORD

nonn

AUTHOR

R. H. Hardin, Apr 07 2012

STATUS

approved