A279735 Number of n X 2 0..1 arrays with no element equal to a strict majority 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, 8, 26, 80, 240, 708, 2062, 5944, 16990, 48220, 136032, 381768, 1066586, 2968040, 8230370, 22751528, 62716752, 172447884, 473081830, 1295113240, 3538749862, 9652296628, 26285128896, 71472896400, 194075990450, 526312559048

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 11 2019: (Start)

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

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

(End)

Example

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

Crossrefs

Column 2 of A279741.

Sequence in context: A302237 A224289 A124721 * A103453 A024023 A295137

Adjacent sequences: A279732 A279733 A279734 * A279736 A279737 A279738

Keyword

nonn

Author

R. H. Hardin, Dec 18 2016

Status

approved