A297901 Number of n X 2 0..1 arrays with every element equal to 0, 1, 3 or 4 king-move adjacent elements, with upper left element zero.

2, 4, 3, 13, 34, 73, 203, 594, 1443, 4013, 11114, 29073, 79243, 216234, 577883, 1566413, 4247794, 11437273, 30940683, 83723074, 225989523, 610970413, 1651964474, 4462848673, 12062978123, 32607525914, 88115865163, 238159441613

Offset

1,1

Comments

Column 2 of A297907.

Links

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

Formula

Empirical: a(n) = a(n-1) + 3*a(n-2) + 8*a(n-3) - 4*a(n-4) - 16*a(n-5) for n>6.

Empirical g.f.: x*(1 + 2*x)*(2 - 2*x - 3*x^2 - 12*x^3 + 12*x^4) / (1 - x - 3*x^2 - 8*x^3 + 4*x^4 + 16*x^5). - Colin Barker, Feb 19 2018

Example

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

Crossrefs

Cf. A297907.

Sequence in context: A257503 A091861 A200715 * A079308 A189825 A271878

Adjacent sequences: A297898 A297899 A297900 * A297902 A297903 A297904

Keyword

nonn

Author

R. H. Hardin, Jan 08 2018

Status

approved