A298163 Number of n X 4 0..1 arrays with every element equal to 3, 4, 5 or 8 king-move adjacent elements, with upper left element zero.

0, 2, 2, 4, 6, 11, 18, 31, 53, 91, 156, 269, 464, 802, 1389, 2410, 4188, 7290, 12709, 22188, 38790, 67902, 119006, 208808, 366763, 644841, 1134799, 1998740, 3523204, 6214955, 10970665, 19377607, 34246676, 60557515, 107134803, 189622060

Offset

1,2

Comments

Column 4 of A298167.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + a(n-2) - a(n-3) - 2*a(n-4) - 2*a(n-5) + a(n-6) + a(n-7).

Empirical g.f.: x^2*(2 - 2*x - 2*x^2 - 2*x^3 + x^4 + 2*x^5) / ((1 - x - x^2)*(1 - x - x^2 - x^3 + x^5)). - Colin Barker, Mar 23 2018

Example

Some solutions for n=8:
..0..0..0..0. .0..0..0..0. .0..0..1..1. .0..0..1..1. .0..0..0..0
..0..0..0..0. .0..0..0..0. .0..0..1..1. .0..0..1..1. .0..0..0..0
..1..1..1..1. .0..0..0..0. .0..0..1..1. .0..0..1..1. .0..0..0..0
..1..1..1..1. .1..1..1..1. .0..1..0..1. .0..0..1..1. .0..0..0..0
..1..1..1..1. .1..1..1..1. .1..0..1..0. .0..0..1..1. .1..1..1..1
..1..1..1..1. .1..1..1..1. .1..1..0..0. .0..0..1..1. .1..1..1..1
..0..0..0..0. .0..0..0..0. .1..1..0..0. .1..1..0..0. .0..0..0..0
..0..0..0..0. .0..0..0..0. .1..1..0..0. .1..1..0..0. .0..0..0..0

Crossrefs

Cf. A298167.

Sequence in context: A124346 A300797 A033961 * A201542 A363251 A000672

Adjacent sequences: A298160 A298161 A298162 * A298164 A298165 A298166

Keyword

nonn

Author

R. H. Hardin, Jan 14 2018

Status

approved