A250554 Number of length n+2 0..1 arrays with the sum of second differences multiplied by some arrangement of +-1 equal to zero.

2, 8, 14, 32, 62, 128, 254, 512, 1022, 2048, 4094, 8192, 16382, 32768, 65534, 131072, 262142, 524288, 1048574, 2097152, 4194302, 8388608, 16777214, 33554432, 67108862, 134217728, 268435454, 536870912, 1073741822, 2147483648, 4294967294

Offset

1,1

Links

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

Formula

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

Empirical: a(n) = 2^(n+1) for even n, 2^(n+1)-2 for odd n.

Empirical g.f.: 2*x*(1 + 2*x - 2*x^2) / ((1 - x)*(1 + x)*(1 - 2*x)). - Colin Barker, Nov 14 2018

Example

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

Crossrefs

Column 1 of A250561.

Sequence in context: A160157 A054598 A031160 * A046959 A086177 A299337

Adjacent sequences: A250551 A250552 A250553 * A250555 A250556 A250557

Keyword

nonn

Author

R. H. Hardin, Nov 25 2014

Status

approved