A279262 Number of n X 2 0..1 arrays with no element equal to a strict majority of its horizontal and vertical neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

0, 4, 10, 20, 38, 68, 120, 208, 358, 612, 1042, 1768, 2992, 5052, 8514, 14324, 24062, 40364, 67624, 113160, 189150, 315844, 526890, 878160, 1462368, 2433268, 4045690, 6721748, 11160278, 18517652, 30706392, 50888128, 84287062, 139531812

Offset

1,2

Comments

Column 2 of A279268.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) - a(n-2) - 3*a(n-3) + a(n-4) + a(n-5).

Conjectures from Colin Barker, Feb 26 2018: (Start)

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

a(n) = (1/25)*(2^(-n)*(-25*2^(2+n)+(50-6*sqrt(5))*(1-sqrt(5))^n + 50*(1+sqrt(5))^n + 6*sqrt(5)*(1+sqrt(5))^n - 5*(1-sqrt(5))^n*(1+sqrt(5))*n + 5*(-1+sqrt(5))*(1+sqrt(5))^n*n)).

(End)

Example

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

Crossrefs

Cf. A279268.

Sequence in context: A038420 A008254 A301178 * A168673 A090164 A261635

Adjacent sequences: A279259 A279260 A279261 * A279263 A279264 A279265

Keyword

nonn

Author

R. H. Hardin, Dec 08 2016

Status

approved