A296798 Number of n X 2 0..1 arrays with each 1 adjacent to 1, 3 or 4 king-move neighboring 1s.

2, 8, 15, 41, 122, 308, 855, 2405, 6522, 18080, 50223, 138353, 383114, 1061116, 2933431, 8119437, 22473514, 62177224, 172075759, 476212281, 1317772378, 3646788996, 10092010711, 27927735285, 77286019354, 213877500592

Offset

1,1

Links

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

Formula

Empirical: a(n) = a(n-1) + 3*a(n-2) + 9*a(n-3) - 4*a(n-4) - 12*a(n-5) - 16*a(n-6).

Empirical g.f.: x*(1 + 2*x)*(2 + 2*x - 3*x^2 - 10*x^3 - 8*x^4) / ((1 - x^2 - 2*x^3)*(1 - x - 2*x^2 - 8*x^3)). - Colin Barker, Feb 25 2019

Example

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

Crossrefs

Column 2 of A296804.

Sequence in context: A082638 A077388 A301986 * A203419 A173287 A167592

Adjacent sequences: A296795 A296796 A296797 * A296799 A296800 A296801

Keyword

nonn

Author

R. H. Hardin, Dec 20 2017

Status

approved