A280118 Number of n X 2 0..2 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

0, 4, 8, 28, 80, 252, 776, 2356, 7200, 21836, 66104, 199652, 601424, 1808252, 5426024, 16253460, 48608384, 145152940, 432853144, 1289129028, 3834701744, 11394112476, 33820033480, 100286009972, 297101633248, 879410116620, 2600884035320

Offset

1,2

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + 7*a(n-2) - 24*a(n-4) - 32*a(n-5) - 16*a(n-6) for n>8.

Empirical g.f.: 4*x^2*(1 - 4*x^2 - 8*x^3 - 2*x^4 + 8*x^5 + 8*x^6) / (1 - x - 4*x^2 - 4*x^3)^2. - Colin Barker, Feb 12 2019

Example

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

Crossrefs

Column 2 of A280124.

Sequence in context: A189546 A059480 A105723 * A143555 A025234 A075308

Adjacent sequences: A280115 A280116 A280117 * A280119 A280120 A280121

Keyword

nonn

Author

R. H. Hardin, Dec 26 2016

Status

approved