A250313 Number of length n+2 0..1 arrays with the sum of second differences squared multiplied by some arrangement of +-1 equal to zero.

2, 8, 8, 24, 42, 104, 212, 464, 950, 1968, 3984, 8072, 16226, 32600, 65324, 130848, 261870, 524000, 1048232, 2096792, 4193882, 8388168, 16776708, 33553904, 67108262, 134217104, 268434752, 536870184, 1073741010, 2147482808, 4294966364

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 3*a(n-1) - 6*a(n-3) + 3*a(n-4) + 3*a(n-5) - 2*a(n-6).

Empirical g.f.: 2*x*(1 + x - 8*x^2 + 6*x^3 + 6*x^4 - 2*x^5) / ((1 - x)^3*(1 + x)^2*(1 - 2*x)). - Colin Barker, Nov 12 2018

Example

Some solutions for n=6:
..1....0....0....0....1....0....0....1....1....0....1....0....0....1....1....0
..1....0....0....1....1....0....1....1....0....0....0....1....1....0....0....0
..0....0....0....0....1....1....0....0....1....0....0....0....0....1....1....1
..0....0....1....0....0....1....1....1....0....1....1....1....0....1....1....1
..1....1....1....0....0....1....0....0....1....1....0....1....1....0....0....1
..0....0....1....0....1....1....0....0....0....1....0....1....1....0....0....0
..0....1....0....1....1....1....1....1....1....1....0....1....0....1....0....1
..0....1....0....0....1....1....0....1....0....1....1....0....1....0....1....1

Crossrefs

Column 1 of A250320.

Sequence in context: A364294 A375853 A146749 * A180825 A230708 A230739

Adjacent sequences: A250310 A250311 A250312 * A250314 A250315 A250316

Keyword

nonn

Author

R. H. Hardin, Nov 18 2014

Status

approved