A297853 Number of n X 3 0..1 arrays with every element equal to 1, 2 or 4 king-move adjacent elements, with upper left element zero.

1, 7, 15, 19, 21, 33, 53, 77, 111, 171, 269, 415, 643, 1013, 1605, 2543, 4041, 6451, 10325, 16547, 26561, 42705, 68741, 110743, 178545, 288053, 464971, 750861, 1212959, 1960023, 3167961, 5121325, 8280457, 13390095, 21655079, 35024669

Offset: 1

Author

R. H. Hardin, Jan 07 2018

Keywords

• nonn

Comments

Column 3 of A297858.

Examples

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

Links

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

Crossrefs

Cf. A297858.

Formula

Empirical: a(n) = 2*a(n-1) - a(n-4) - a(n-5) - a(n-6) + a(n-7) + a(n-8) for n>9.

Empirical g.f.: x*(1 + 5*x + x^2 - 11*x^3 - 16*x^4 - x^5 + 10*x^6 + 11*x^7 + 4*x^8) / ((1 - x)*(1 + x^2)*(1 - x - x^2)*(1 - x^2 - x^3)). - Colin Barker, Mar 22 2018