A211469 Number of (n+1)X(n+1) -8..8 symmetric matrices with every 2X2 subblock having sum zero and two or three distinct values

144, 380, 856, 1808, 3706, 7454, 14786, 29300, 57442, 113394, 221676, 437914, 857230, 1698058, 3335170, 6630316, 13078566, 26101324, 51724674, 103628922, 206316160, 414882652, 829705256, 1674253282, 3362428628, 6806756646

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) +20*a(n-2) -64*a(n-3) -172*a(n-4) +598*a(n-5) +826*a(n-6) -3213*a(n-7) -2390*a(n-8) +10954*a(n-9) +4103*a(n-10) -24660*a(n-11) -3463*a(n-12) +36968*a(n-13) -524*a(n-14) -36330*a(n-15) +4151*a(n-16) +22474*a(n-17) -3786*a(n-18) -8144*a(n-19) +1410*a(n-20) +1540*a(n-21) -180*a(n-22) -120*a(n-23)

Example

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

Crossrefs

Sequence in context: A189988 A232892 A034285 * A248551 A178972 A250787

Adjacent sequences: A211466 A211467 A211468 * A211470 A211471 A211472

Keyword

nonn

Author

R. H. Hardin Apr 12 2012

Status

approved