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A211114 Number of (n+1) X (n+1) -2..2 symmetric matrices with every 2 X 2 subblock having sum zero and one or three distinct values. 1
9, 19, 39, 81, 167, 341, 695, 1405, 2839, 5709, 11479, 23021, 46167, 92461, 185175, 370605, 741719, 1483949, 2968919, 5938861, 11879767, 23761581, 47527255, 95058605, 190125399, 380258989, 760534359, 1521085101, 3042202967, 6084438701 (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) = 2*a(n-1) + 3*a(n-2) - 6*a(n-3) - 2*a(n-4) + 4*a(n-5).

Empirical g.f.: x*(9 + x - 26*x^2 + 20*x^4) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 - 2*x^2)). - Colin Barker, Jul 15 2018

EXAMPLE

Some solutions for n=3:

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

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

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

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

CROSSREFS

Sequence in context: A145958 A290245 A039299 * A159697 A014005 A286624

Adjacent sequences:  A211111 A211112 A211113 * A211115 A211116 A211117

KEYWORD

nonn

AUTHOR

R. H. Hardin, Apr 02 2012

STATUS

approved

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Last modified September 20 08:10 EDT 2021. Contains 347577 sequences. (Running on oeis4.)