A211497 Number of (n+1)X(n+1) -4..4 symmetric matrices with every 2X2 subblock having sum zero and two, three or four distinct values

40, 180, 808, 3636, 16396, 74104, 335660, 1523420, 6925768, 31527492, 143656108, 654965928, 2986993420, 13622286844, 62110476152, 283072002980, 1289383564204, 5869109209272, 26695147549612, 121321864635996, 550906942638568

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..162

Formula

Empirical: a(n) = 21*a(n-1) -177*a(n-2) +742*a(n-3) -1477*a(n-4) +665*a(n-5) +1725*a(n-6) -952*a(n-7) -1462*a(n-8) -476*a(n-9) -48*a(n-10)

Example

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

Crossrefs

Sequence in context: A264547 A327430 A251210 * A251203 A187510 A187379

Adjacent sequences: A211494 A211495 A211496 * A211498 A211499 A211500

Keyword

nonn

Author

R. H. Hardin Apr 13 2012

Status

approved