A296551 Number of n X 5 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 3 or 6 neighboring 1s.

1, 1, 4, 7, 11, 18, 34, 59, 100, 174, 309, 538, 930, 1620, 2835, 4941, 8596, 14980, 26129, 45536, 79328, 138252, 240988, 419984, 731872, 1275492, 2222988, 3874156, 6751645, 11766605, 20506721, 35738549, 62283936, 108546855, 189173003, 329685682

Offset

1,3

Links

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

Formula

Empirical: a(n) = a(n-1) + 3*a(n-4) + a(n-6) + 3*a(n-7) + a(n-10).

Empirical g.f.: x*(1 + 3*x^2 + 3*x^3 + x^4 + 4*x^5 + 3*x^6 + x^8 + x^9) / ((1 + x)*(1 - x + x^2)*(1 - x - x^3 - 2*x^4 - x^7)). - Colin Barker, Feb 23 2019

Example

Some solutions for n=7:
..0..0..0..0..0. .0..0..0..0..0. .0..0..0..0..0. .0..0..1..1..0
..0..0..0..0..0. .0..1..1..0..0. .0..0..1..1..0. .0..1..1..1..0
..0..0..0..0..0. .1..1..1..0..0. .0..1..1..1..0. .0..1..1..0..0
..0..0..0..1..1. .1..1..0..1..1. .0..1..1..0..0. .0..0..0..0..0
..0..0..1..1..1. .0..0..1..1..1. .0..0..0..1..1. .0..0..0..0..0
..0..0..1..1..0. .0..0..1..1..0. .0..0..1..1..1. .0..0..0..0..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 A296554.

Sequence in context: A023502 A274286 A024882 * A087203 A310768 A109328

Adjacent sequences: A296548 A296549 A296550 * A296552 A296553 A296554

Keyword

nonn

Author

R. H. Hardin, Dec 15 2017

Status

approved