A211335 Number of (n+1)X(n+1) -5..5 symmetric matrices with every 2X2 subblock having sum zero and one, three or four distinct values

47, 203, 851, 3551, 14747, 61279, 255139, 1066031, 4472467, 18846943, 79770595, 339053711, 1446716915, 6194800095, 26609084003, 114610153487, 494820389939, 2140706570911, 9277278747747, 40264500902671, 174969241485427

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) = 13*a(n-1) -40*a(n-2) -130*a(n-3) +771*a(n-4) +305*a(n-5) -5330*a(n-6) +176*a(n-7) +18744*a(n-8) +2324*a(n-9) -31120*a(n-10) -14864*a(n-11) +9312*a(n-12) +3072*a(n-13) -1152*a(n-14)

Example

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

Crossrefs

Sequence in context: A157362 A141874 A224325 * A142203 A067986 A141537

Adjacent sequences: A211332 A211333 A211334 * A211336 A211337 A211338

Keyword

nonn

Author

R. H. Hardin Apr 07 2012

Status

approved