A211330 Number of (n+1) X (n+1) -5..5 symmetric matrices with every 2 X 2 subblock having sum zero and three distinct values.

46, 90, 172, 316, 588, 1070, 1974, 3608, 6670, 12310, 22930, 42818, 80560, 152240, 289462, 553112, 1062084, 2049116, 3968676, 7718410, 15055782, 29469492, 57813502, 113731682, 224119946, 442604110, 875210760, 1733534748, 3436966638

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) - a(n-2) - 31*a(n-3) + 39*a(n-4) + 56*a(n-5) - 116*a(n-6) - 14*a(n-7) + 115*a(n-8) - 34*a(n-9) - 30*a(n-10) + 12*a(n-11).

Empirical g.f.: 2*x*(23 - 70*x - 116*x^2 + 486*x^3 + 88*x^4 - 1154*x^5 + 298*x^6 + 1082*x^7 - 466*x^8 - 309*x^9 + 142*x^10) / ((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.
.-1..2.-1..0...-5..2.-5..1...-1..2.-1..2....0.-1.-1.-1...-1..2..2..0
..2.-3..2.-1....2..1..2..2....2.-3..2.-3...-1..2..0..2....2.-3.-1.-1
.-1..2.-1..0...-5..2.-5..1...-1..2.-1..2...-1..0.-2..0....2.-1..5.-3
..0.-1..0..1....1..2..1..3....2.-3..2.-3...-1..2..0..2....0.-1.-3..1

Crossrefs

Sequence in context: A057454 A260278 A234260 * A121929 A007630 A004923

Adjacent sequences: A211327 A211328 A211329 * A211331 A211332 A211333

Keyword

nonn

Author

R. H. Hardin, Apr 07 2012

Status

approved