A208284 Number of n X 5 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 1 0 vertically.

16, 256, 1260, 3984, 9900, 21096, 40376, 71360, 118584, 187600, 285076, 418896, 598260, 833784, 1137600, 1523456, 2006816, 2604960, 3337084, 4224400, 5290236, 6560136, 8061960, 9825984, 11885000, 14274416, 17032356, 20199760, 23820484

Offset

1,1

Comments

Column 5 of A208287.

Links

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

Formula

Empirical: a(n) = (5/6)*n^5 + 9*n^4 + (91/6)*n^3 - 9*n^2.

Conjectures from Colin Barker, Jun 29 2018: (Start)

G.f.: 4*x*(2 - x)*(2 + 21*x + 6*x^2 - 4*x^3) / (1 - x)^6.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.

(End)

Example

Some solutions for n=4:
..0..1..0..1..0....0..1..0..1..0....0..1..0..1..1....1..0..1..1..1
..1..0..1..0..0....1..1..0..1..1....0..1..0..1..0....0..1..0..1..1
..1..1..0..1..0....1..1..0..1..0....0..1..0..1..0....0..1..1..1..1
..1..1..0..1..0....1..1..0..1..0....0..1..0..1..0....0..1..1..1..1

Crossrefs

Cf. A208287.

Sequence in context: A207951 A207860 A207810 * A208417 A208025 A207805

Adjacent sequences: A208281 A208282 A208283 * A208285 A208286 A208287

Keyword

nonn

Author

R. H. Hardin, Feb 25 2012

Status

approved