A297296 Number of n X 5 0..1 arrays with every 1 horizontally or antidiagonally adjacent to 2 neighboring 1s.

1, 4, 9, 21, 49, 114, 266, 620, 1446, 3372, 7864, 18340, 42772, 99752, 232640, 542560, 1265352, 2951040, 6882384, 16051024, 37434032, 87303264, 203607776, 474851968, 1107444896, 2582771648, 6023513600, 14047976768, 32762547648, 76408478336

Offset

1,2

Links

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

Formula

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

Empirical g.f.: x*(1 + x)*(1 + x - 2*x^2 - x^3) / (1 - 2*x - 2*x^2 + 2*x^3 + 2*x^4). - Colin Barker, Feb 26 2019

Example

Some solutions for n=5:
..0..0..0..0..0. .0..0..0..0..0. .0..0..0..0..0. .0..0..0..1..1
..0..0..1..1..0. .0..0..1..1..1. .0..0..0..0..0. .0..0..1..1..0
..0..1..1..0..0. .0..1..0..1..0. .0..0..0..0..0. .0..0..0..1..1
..0..0..0..0..0. .1..1..1..0..0. .0..0..0..1..1. .0..0..1..1..0
..0..0..0..0..0. .0..0..0..0..0. .0..0..1..1..0. .0..0..0..0..0

Crossrefs

Column 5 of A297299.

Sequence in context: A084861 A122498 A132750 * A048582 A069231 A243635

Adjacent sequences: A297293 A297294 A297295 * A297297 A297298 A297299

Keyword

nonn

Author

R. H. Hardin, Dec 27 2017

Status

approved