A211493 Number of (n+1)X(n+1) -4..4 symmetric matrices with every 2X2 subblock having sum zero and two or three distinct values

40, 96, 214, 446, 920, 1852, 3716, 7414, 14772, 29486, 58836, 117908, 236354, 475986, 959170, 1940794, 3930106, 7985174, 16237818, 33106698, 67555856, 138133826, 282669656, 579365960, 1188357854, 2440574368, 5015738686, 10318671714

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) +8*a(n-2) -47*a(n-3) -13*a(n-4) +224*a(n-5) -60*a(n-6) -553*a(n-7) +282*a(n-8) +745*a(n-9) -465*a(n-10) -524*a(n-11) +351*a(n-12) +165*a(n-13) -112*a(n-14) -18*a(n-15) +12*a(n-16)

Example

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

Crossrefs

Sequence in context: A038466 A279689 A063310 * A185791 A092889 A235280

Adjacent sequences: A211490 A211491 A211492 * A211494 A211495 A211496

Keyword

nonn

Author

R. H. Hardin Apr 13 2012

Status

approved