A297883 Number of n X 2 0..1 arrays with every element equal to 0, 1, 2 or 4 king-move adjacent elements, with upper left element zero.

2, 7, 13, 29, 69, 137, 301, 705, 1461, 3193, 7373, 15729, 34405, 78569, 170813, 374945, 849493, 1868953, 4119725, 9284817, 20576325, 45534025, 102285085, 227659265, 505431861, 1133187833, 2528544397, 5627807793, 12604474149, 28165860265

Offset

1,1

Comments

Column 2 of A297889.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) - 2*a(n-2) + 8*a(n-3) - 20*a(n-4) + 8*a(n-5) for n>6.

Empirical g.f.: x*(2 + x - 4*x^2 - 12*x^3 - 8*x^4 + 8*x^5) / ((1 - 2*x)*(1 - x - 8*x^3 + 4*x^4)). - Colin Barker, Feb 19 2018

Example

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

Crossrefs

Cf. A297889.

Sequence in context: A183435 A360385 A141777 * A215206 A298215 A127396

Adjacent sequences: A297880 A297881 A297882 * A297884 A297885 A297886

Keyword

nonn

Author

R. H. Hardin, Jan 07 2018

Status

approved