A211711 Number of (n+1)X(n+1) -11..11 symmetric matrices with every 2X2 subblock having sum zero and three distinct values

230, 516, 1030, 1908, 3528, 6312, 11390, 20316, 36520, 65646, 118702, 216006, 394802, 728492, 1348550, 2522796, 4730304, 8960110, 16997998, 32539860, 62348810, 120381720, 232534604, 451979570, 878630354, 1716513328, 3353186654

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) = 6*a(n-1) +3*a(n-2) -83*a(n-3) +92*a(n-4) +443*a(n-5) -868*a(n-6) -1073*a(n-7) +3394*a(n-8) +748*a(n-9) -7085*a(n-10) +1842*a(n-11) +8231*a(n-12) -4528*a(n-13) -5075*a(n-14) +3936*a(n-15) +1424*a(n-16) -1511*a(n-17) -121*a(n-18) +244*a(n-19) -6*a(n-20) -12*a(n-21)

Example

Some solutions for n=3
..1..2.-5..2...-8..2.-8..3...11.-7..3.-5....7.-8..7.-8....5..1..1..1
..2.-5..8.-5....2..4..2..3...-7..3..1..1...-8..9.-8..9....1.-7..5.-7
.-5..8-11..8...-8..2.-8..3....3..1.-5..3....7.-8..7.-8....1..5.-3..5
..2.-5..8.-5....3..3..3..2...-5..1..3.-1...-8..9.-8..9....1.-7..5.-7

Crossrefs

Sequence in context: A215217 A291617 A304389 * A211716 A251445 A251283

Adjacent sequences: A211708 A211709 A211710 * A211712 A211713 A211714

Keyword

nonn

Author

R. H. Hardin Apr 20 2012

Status

approved