A211260 Number of (n+1)X(n+1) -6..6 symmetric matrices with every 2X2 subblock having sum zero and two, three or four distinct values

84, 546, 3552, 23154, 151218, 989484, 6486618, 42598386, 280208436, 1845953430, 12177085710, 80422381488, 531677196078, 3517904882982, 23292441203544, 154303014921810, 1022587652767170, 6778549963517052, 44939890595804202

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..159

Formula

Empirical: a(n) = 44*a(n-1) -834*a(n-2) +8822*a(n-3) -56045*a(n-4) +210804*a(n-5) -405935*a(n-6) +122980*a(n-7) +727296*a(n-8) -286484*a(n-9) -957331*a(n-10) -589182*a(n-11) -162870*a(n-12) -21384*a(n-13) -1080*a(n-14)

Example

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

Crossrefs

Sequence in context: A329935 A233055 A233056 * A233053 A220203 A008429

Adjacent sequences: A211257 A211258 A211259 * A211261 A211262 A211263

Keyword

nonn

Author

R. H. Hardin Apr 06 2012

Status

approved