A297220 Number of n X 4 0..1 arrays with every 1 horizontally or antidiagonally adjacent to 1 neighboring 1s.

4, 16, 57, 207, 751, 2720, 9861, 35741, 129540, 469528, 1701805, 6168220, 22356839, 81032722, 293704534, 1064537220, 3858433620, 13984959985, 50688731051, 183722188635, 665904273716, 2413581640617, 8748068704189, 31707527421628

Offset

1,1

Links

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

Formula

Empirical: a(n) = a(n-1) + 6*a(n-2) + 11*a(n-3) + 6*a(n-4) + a(n-5).

Empirical g.f.: x*(2 + x)^2*(1 + 2*x + 2*x^2) / (1 - x - 6*x^2 - 11*x^3 - 6*x^4 - x^5). - Colin Barker, Feb 26 2019

Example

Some solutions for n=7:
..0..0..1..1. .0..0..0..0. .0..0..0..0. .0..0..1..0. .0..1..0..0
..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..1..0..0. .1..0..0..0
..1..1..0..0. .0..1..0..1. .0..1..0..0. .0..1..0..1. .1..1..0..1
..0..0..1..0. .1..0..1..0. .1..0..0..0. .1..0..1..0. .0..0..1..0
..0..1..0..0. .0..0..0..0. .1..1..0..0. .0..0..1..1. .0..0..1..1
..0..1..0..1. .0..0..0..0. .0..1..0..1. .0..0..0..0. .0..0..0..0
..1..0..1..0. .0..0..1..1. .1..0..1..0. .1..1..0..0. .1..1..0..0

Crossrefs

Column 4 of A297224.

Sequence in context: A281064 A122032 A197674 * A297375 A283124 A282393

Adjacent sequences: A297217 A297218 A297219 * A297221 A297222 A297223

Keyword

nonn

Author

R. H. Hardin, Dec 27 2017

Status

approved