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

1,2

Comments

Column 3 of A297858.

Links

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

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

Example

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

Crossrefs

Cf. A297858.

Sequence in context: A275190 A224891 A138641 * A298050 A115783 A140109

Adjacent sequences: A297850 A297851 A297852 * A297854 A297855 A297856

Keyword

nonn

Author

R. H. Hardin, Jan 07 2018

Status

approved