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A211115 Number of (n+1) X (n+1) -2..2 symmetric matrices with every 2 X 2 subblock having sum zero and two or three distinct values. 1
12, 26, 54, 106, 208, 398, 766, 1458, 2792, 5324, 10206, 19550, 37616, 72446, 140048, 271194, 526792, 1025268, 2000636, 3911284, 7663264, 15040266, 29571962, 58231566, 114837690, 226761020, 448318274, 887305854, 1757921506, 3485905204 (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) = 5*a(n-1) - 4*a(n-2) - 16*a(n-3) + 27*a(n-4) + 8*a(n-5) - 35*a(n-6) + 10*a(n-7) + 10*a(n-8) - 4*a(n-9).

Empirical g.f.: 2*x*(6 - 17*x - 14*x^2 + 66*x^3 - 7*x^4 - 76*x^5 + 29*x^6 + 22*x^7 - 10*x^8) / ((1 - x)*(1 - 2*x)*(1 - x - x^2)*(1 - 2*x^2)*(1 - x - 2*x^2 + x^3)). - Colin Barker, Jul 15 2018

EXAMPLE

Some solutions for n=3:

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

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

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

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

CROSSREFS

Sequence in context: A119412 A105814 A297427 * A232936 A274897 A030736

Adjacent sequences:  A211112 A211113 A211114 * A211116 A211117 A211118

KEYWORD

nonn

AUTHOR

R. H. Hardin, Apr 02 2012

STATUS

approved

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Last modified April 22 22:16 EDT 2019. Contains 322378 sequences. (Running on oeis4.)