A281028 Number of n X 2 0..1 arrays with no element equal to more than three of its king-move neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

0, 0, 2, 12, 58, 252, 1048, 4204, 16454, 63236, 239622, 897792, 3332864, 12277952, 44938282, 163566412, 592492026, 2137194788, 7680594760, 27511516436, 98254943022, 349979793492, 1243627373550, 4409519905928, 15603737422416

Offset

1,3

Links

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

Formula

Empirical: a(n) = 6*a(n-1) - 7*a(n-2) - 2*a(n-3) - 17*a(n-4) + 24*a(n-6) + 16*a(n-7) + 12*a(n-8) - 16*a(n-9) - 16*a(n-10).

Empirical g.f.: 2*x^3*(1 - 2*x^3)^2 / (1 - 3*x - x^2 - 2*x^3 + 2*x^4 + 4*x^5)^2. - Colin Barker, Feb 15 2019

Example

Some solutions for n=4:
..0..0. .0..0. .0..0. .0..0. .0..1. .0..0. .0..0. .0..1. .0..0. .0..1
..0..1. .1..1. .1..0. .1..1. .1..1. .1..0. .0..1. .0..0. .1..0. .1..1
..0..0. .0..1. .0..0. .1..0. .0..1. .0..0. .0..0. .0..1. .0..0. .1..0
..0..1. .1..1. .1..1. .1..1. .1..1. .1..0. .1..0. .0..0. .0..1. .1..1

Crossrefs

Column 2 of A281034.

Sequence in context: A094780 A268594 A100103 * A054145 A285364 A282435

Adjacent sequences: A281025 A281026 A281027 * A281029 A281030 A281031

Keyword

nonn

Author

R. H. Hardin, Jan 13 2017

Status

approved