A281199 Number of n X 2 0..1 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

0, 2, 10, 38, 130, 420, 1308, 3970, 11822, 34690, 100610, 289032, 823800, 2332418, 6566290, 18394910, 51310978, 142587180, 394905492, 1090444930, 3002921270, 8249479162, 22612505090, 61857842448, 168903452400, 460409998850

Offset

1,2

Links

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

Formula

Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) - a(n-4).

Conjectures from Colin Barker, Feb 16 2019: (Start)

G.f.: 2*x^2*(1 - x) / (1 - 3*x + x^2)^2.

a(n) = (2^(-n)*(2*sqrt(5)*((3-sqrt(5))^n - (3+sqrt(5))^n) - 5*(3-sqrt(5))^n*(1+sqrt(5))*n + 5*(-1+sqrt(5))*(3+sqrt(5))^n*n)) / 25.

(End)

Example

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

Crossrefs

Column 2 of A281205.

Sequence in context: A048499 A119358 A110148 * A056182 A081956 A120278

Adjacent sequences: A281196 A281197 A281198 * A281200 A281201 A281202

Keyword

nonn

Author

R. H. Hardin, Jan 17 2017

Status

approved