A211815 Number of (n+1)X(n+1) -10..10 symmetric matrices with every 2X2 subblock having sum zero and one or three distinct values

189, 435, 881, 1701, 3247, 6081, 11421, 21369, 40139, 75675, 143095, 272447, 519721, 999049, 1922557, 3726521, 7226935, 14102879, 27524803, 53995609, 105915029, 208603523, 410770735, 811441587, 1602540065, 3172707173, 6279776411

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) = 5*a(n-1) +8*a(n-2) -75*a(n-3) +16*a(n-4) +465*a(n-5) -403*a(n-6) -1541*a(n-7) +1945*a(n-8) +2941*a(n-9) -4737*a(n-10) -3219*a(n-11) +6630*a(n-12) +1827*a(n-13) -5437*a(n-14) -299*a(n-15) +2516*a(n-16) -186*a(n-17) -591*a(n-18) +94*a(n-19) +54*a(n-20) -12*a(n-21)

Example

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

Crossrefs

Sequence in context: A224674 A076759 A348544 * A347390 A292173 A231394

Adjacent sequences: A211812 A211813 A211814 * A211816 A211817 A211818

Keyword

nonn

Author

R. H. Hardin Apr 21 2012

Status

approved