A211332 Number of (n+1)X(n+1) -5..5 symmetric matrices with every 2X2 subblock having sum zero and two or three distinct values

60, 144, 312, 630, 1266, 2474, 4864, 9466, 18544, 36252, 71260, 140314, 277456, 550506, 1095678, 2189478, 4384860, 8817146, 17756308, 35895256, 72635652, 147493822, 299688524, 610819886, 1245448294, 2546376998, 5207461228

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) +467*a(n-5) -412*a(n-6) -1551*a(n-7) +2039*a(n-8) +2909*a(n-9) -5118*a(n-10) -2897*a(n-11) +7385*a(n-12) +976*a(n-13) -6197*a(n-14) +720*a(n-15) +2888*a(n-16) -760*a(n-17) -674*a(n-18) +236*a(n-19) +60*a(n-20) -24*a(n-21)

Example

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

Crossrefs

Sequence in context: A043478 A044311 A044692 * A039497 A218243 A218392

Adjacent sequences: A211329 A211330 A211331 * A211333 A211334 A211335

Keyword

nonn

Author

R. H. Hardin Apr 07 2012

Status

approved