A211468 Number of (n+1)X(n+1) -8..8 symmetric matrices with every 2X2 subblock having sum zero and one or three distinct values

121, 277, 565, 1101, 2135, 4047, 7739, 14661, 28031, 53463, 102733, 197579, 382143, 740723, 1441747, 2813157, 5505551, 10799509, 21229339, 41813647, 82481877, 162964213, 322323737, 638333051, 1265124641, 2509927951, 4982252633

Offset

1,1

Comments

Symmetry and 2X2 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) = 3*a(n-1) +13*a(n-2) -43*a(n-3) -68*a(n-4) +255*a(n-5) +185*a(n-6) -810*a(n-7) -289*a(n-8) +1487*a(n-9) +292*a(n-10) -1577*a(n-11) -242*a(n-12) +895*a(n-13) +170*a(n-14) -210*a(n-15) -60*a(n-16)

Example

Some solutions for n=3
.-1..3.-1..3...-8..0.-4..8...-4.-2.-2.-2...-3..5.-3..5....8.-6..1.-6
..3.-5..3.-5....0..8.-4..0...-2..8.-4..8....5.-7..5.-7...-6..4..1..4
.-1..3.-1..3...-4.-4..0..4...-2.-4..0.-4...-3..5.-3..5....1..1.-6..1
..3.-5..3.-5....8..0..4.-8...-2..8.-4..8....5.-7..5.-7...-6..4..1..4

Crossrefs

Sequence in context: A088285 A218172 A083749 * A023696 A038467 A106562

Adjacent sequences: A211465 A211466 A211467 * A211469 A211470 A211471

Keyword

nonn

Author

R. H. Hardin Apr 12 2012

Status

approved