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A211331 Number of (n+1) X (n+1) -5..5 symmetric matrices with every 2 X 2 subblock having sum zero and one or three distinct values. 1
47, 99, 201, 397, 789, 1531, 2999, 5801, 11307, 21927, 42763, 83311, 162977, 319089, 626611, 1232377, 2429037, 4795401, 9482053, 18776315, 37223555, 73884069, 146773655, 291853839, 580697115, 1156276783, 2303407301, 4591264605 (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) - 32*a(n-3) + 8*a(n-4) + 95*a(n-5) - 60*a(n-6) - 130*a(n-7) + 101*a(n-8) + 81*a(n-9) - 64*a(n-10) - 18*a(n-11) + 12*a(n-12).

Empirical g.f.: x*(47 - 89*x - 383*x^2 + 701*x^3 + 1189*x^4 - 2038*x^5 - 1770*x^6 + 2708*x^7 + 1255*x^8 - 1596*x^9 - 340*x^10 + 296*x^11) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 - x - x^2)*(1 - 2*x^2)*(1 - 3*x^2)*(1 - x - 2*x^2 + x^3)). - Colin Barker, Jul 17 2018

EXAMPLE

Some solutions for n=3:

.-5..4.-3..4....0.-1.-1..0...-3..2.-1..2....0..0..0..2....3.-2..3..1

..4.-3..2.-3...-1..2..0..1....2.-1..0.-1....0..0..0.-2...-2..1.-2.-2

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

..4.-3..2.-3....0..1..1..0....2.-1..0.-1....2.-2..2.-4....1.-2..1.-5

CROSSREFS

Sequence in context: A176134 A155844 A245688 * A141961 A142661 A216067

Adjacent sequences:  A211328 A211329 A211330 * A211332 A211333 A211334

KEYWORD

nonn

AUTHOR

R. H. Hardin, Apr 07 2012

STATUS

approved

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Last modified September 18 12:00 EDT 2019. Contains 327170 sequences. (Running on oeis4.)