A296798 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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