A279523 Number of n X 2 0..2 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, 46, 384, 2894, 20444, 138944, 918744, 5954690, 38005496, 239638474, 1496190304, 9265675104, 56988880140, 348469302678, 2120061738416, 12841720934726, 77485235860420, 465936438401536, 2793228811996384

Offset

1,2

Comments

Column 2 of A279527.

Links

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

Formula

Empirical: a(n) = 12*a(n-1) - 36*a(n-2) - 22*a(n-3) + 140*a(n-4) - 48*a(n-5) - 121*a(n-6) + 88*a(n-7) - 16*a(n-8).

Empirical g.f.: 2*x^2*(1 - x)*(2 + x - 11*x^2 + 4*x^3) / (1 - 6*x + 11*x^3 - 4*x^4)^2. - Colin Barker, Feb 26 2018

Example

Some solutions for n=4:
..0..1. .0..0. .0..1. .0..0. .0..1. .0..1. .0..1. .0..1. .0..0. .0..1
..2..1. .1..2. .2..0. .1..1. .1..2. .0..2. .0..0. .1..0. .1..1. .2..2
..0..1. .2..0. .1..1. .1..2. .2..2. .2..2. .0..1. .0..0. .2..1. .1..2
..1..2. .2..2. .0..1. .0..0. .0..0. .0..1. .2..1. .1..1. .2..0. .1..0

Crossrefs

Cf. A279527.

Sequence in context: A273776 A131540 A218997 * A194488 A132932 A231787

Adjacent sequences: A279520 A279521 A279522 * A279524 A279525 A279526

Keyword

nonn

Author

R. H. Hardin, Dec 14 2016

Status

approved