A297852 Number of n X 2 0..1 arrays with every element equal to 1, 2 or 4 king-move adjacent elements, with upper left element zero.

1, 3, 7, 13, 23, 49, 95, 177, 359, 705, 1351, 2689, 5303, 10321, 20423, 40353, 79223, 156657, 309991, 611713, 1210967, 2399761, 4750919, 9419937, 18694199, 37092657, 73659175, 146373313, 290909975, 578470225, 1150862855, 2290191585, 4559123447

Offset

1,2

Comments

Column 2 of A297858.

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) + 4*a(n-3) - 10*a(n-4) + 4*a(n-5) for n>6.

Empirical g.f.: x*(1 - 6*x^3 - 4*x^4 + 4*x^5) / ((1 - 2*x)*(1 - x - 4*x^3 + 2*x^4)). - Colin Barker, Feb 19 2018

Example

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

Crossrefs

Cf. A297858.

Sequence in context: A049112 A349793 A100720 * A297953 A084898 A147380

Adjacent sequences: A297849 A297850 A297851 * A297853 A297854 A297855

Keyword

nonn

Author

R. H. Hardin, Jan 07 2018

Status

approved