A279897 Number of n X 3 0..2 arrays with no element unequal to a strict majority of its king-move neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

2, 6, 9, 20, 43, 94, 213, 456, 1003, 2146, 4625, 9852, 20983, 44438, 93917, 197808, 415683, 871370, 1822889, 3805924, 7932303, 16505342, 34292341, 71147800, 147422043, 305096754, 630699073, 1302409036, 2686840103, 5537724006

Offset

1,1

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + 3*a(n-2) - 4*a(n-3) - 4*a(n-4) for n>7.

Conjectures from Colin Barker, Feb 12 2019: (Start)

G.f.: x*(2 + 2*x - 9*x^2 - 8*x^3 + 8*x^4 + 8*x^5 + 12*x^6) / ((1 + x)^2*(1 - 2*x)^2).

a(n) = (1280*(-1)^n + 31*2^(2+n) - 264*(-1)^n*n + 33*2^n*n) / 216 for n>3.

(End)

Example

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

Crossrefs

Column 3 of A279902.

Sequence in context: A350949 A088902 A265016 * A336131 A095967 A316429

Adjacent sequences: A279894 A279895 A279896 * A279898 A279899 A279900

Keyword

nonn

Author

R. H. Hardin, Dec 22 2016

Status

approved