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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. 1
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 (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..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

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Last modified October 16 02:52 EDT 2019. Contains 328038 sequences. (Running on oeis4.)