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A211323 Number of (n+1) X (n+1) -3..3 symmetric matrices with every 2 X 2 subblock having sum zero and three distinct values. 1
14, 24, 42, 76, 140, 262, 496, 948, 1826, 3540, 6900, 13510, 26552, 52348, 103474, 204972, 406748, 808326, 1608288, 3203044, 6384194, 12732964, 25408612, 50724486, 101298920, 202355052, 404317266, 807998908, 1614969356, 3228274630 (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) = 4*a(n-1) - 4*a(n-2) - a(n-3) + 2*a(n-4).

Empirical g.f.: 2*x*(7 - 16*x + x^2 + 9*x^3) / ((1 - x)*(1 - 2*x)*(1 - x - x^2)). - Colin Barker, Jul 16 2018

EXAMPLE

Some solutions for n=3.

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

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

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

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

CROSSREFS

Sequence in context: A111743 A164399 A164404 * A141838 A140499 A068365

Adjacent sequences:  A211320 A211321 A211322 * A211324 A211325 A211326

KEYWORD

nonn

AUTHOR

R. H. Hardin, Apr 07 2012

STATUS

approved

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Last modified September 20 12:05 EDT 2021. Contains 347586 sequences. (Running on oeis4.)