A211496 Number of (n+1)X(n+1) -4..4 symmetric matrices with every 2X2 subblock having sum zero and one, three or four distinct values

29, 105, 385, 1437, 5353, 19901, 73617, 271149, 994593, 3635837, 13253649, 48203469, 174998977, 634413757, 2297355217, 8312124813, 30054882625, 108619779773, 392421136145, 1417398932429, 5118773127873, 18484336915517

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) = 12*a(n-1) -36*a(n-2) -86*a(n-3) +557*a(n-4) -82*a(n-5) -2844*a(n-6) +1812*a(n-7) +6764*a(n-8) -4000*a(n-9) -7184*a(n-10) +1824*a(n-11) +1408*a(n-12) -384*a(n-13)

Example

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

Crossrefs

Sequence in context: A126554 A258721 A009406 * A233049 A233050 A142176

Adjacent sequences: A211493 A211494 A211495 * A211497 A211498 A211499

Keyword

nonn

Author

R. H. Hardin Apr 13 2012

Status

approved