A211255 Number of (n+1)X(n+1) -6..6 symmetric matrices with every 2X2 subblock having sum zero and one or three distinct values

65, 143, 287, 567, 1109, 2145, 4163, 8041, 15609, 30271, 58955, 114925, 224757, 440281, 864529, 1700629, 3351109, 6614459, 13071953, 25871279, 51248961, 101644005, 201725287, 400751925, 796518335, 1584431751, 3152835011

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) = 4*a(n-1) +5*a(n-2) -36*a(n-3) +5*a(n-4) +123*a(n-5) -69*a(n-6) -205*a(n-7) +150*a(n-8) +176*a(n-9) -138*a(n-10) -74*a(n-11) +56*a(n-12) +12*a(n-13) -8*a(n-14)

Example

Some solutions for n=3
..4.-3..4.-5....4.-2..4.-2....1..0.-1.-3....2.-1..0..1...-6..4.-2..0
.-3..2.-3..4...-2..0.-2..0....0.-1..2..2...-1..0..1.-2....4.-2..0..2
..4.-3..4.-5....4.-2..4.-2...-1..2.-3.-1....0..1.-2..3...-2..0..2.-4
.-5..4.-5..6...-2..0.-2..0...-3..2.-1..5....1.-2..3.-4....0..2.-4..6

Crossrefs

Sequence in context: A285300 A194002 A092226 * A297849 A226926 A345700

Adjacent sequences: A211252 A211253 A211254 * A211256 A211257 A211258

Keyword

nonn

Author

R. H. Hardin Apr 06 2012

Status

approved