A211334 Number of (n+1)X(n+1) -5..5 symmetric matrices with every 2X2 subblock having sum zero and three or four distinct values

46, 194, 802, 3322, 13754, 57170, 238650, 1001306, 4222530, 17893954, 76173162, 325583338, 1396612370, 6009460210, 25926690010, 112107619226, 485673993154, 2107375609954, 9156123643082, 39825088001994, 173378643531634

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) = 8*a(n-1) -114*a(n-3) +81*a(n-4) +646*a(n-5) -276*a(n-6) -1588*a(n-7) -180*a(n-8) +672*a(n-9) -144*a(n-10)

Example

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

Crossrefs

Sequence in context: A251460 A235767 A192850 * A160334 A235550 A083358

Adjacent sequences: A211331 A211332 A211333 * A211335 A211336 A211337

Keyword

nonn

Author

R. H. Hardin Apr 07 2012

Status

approved