A280474 Number of n X 2 0..2 arrays with no element unequal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

1, 6, 30, 158, 846, 4446, 22734, 113310, 552654, 2647390, 12492366, 58202526, 268228430, 1224529758, 5544352206, 24921415326, 111297979854, 494186360670, 2182903872334, 9596971862430, 42012203555406, 183197641092446

Offset

1,2

Links

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

Formula

Empirical: a(n) = 15*a(n-1) - 87*a(n-2) + 245*a(n-3) - 348*a(n-4) + 240*a(n-5) - 64*a(n-6).

Conjectures from Colin Barker, Feb 13 2019: (Start)

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

a(n) = (8*(4^n-1) + 21*4^n*n + 6*(32+4^n)*n^2) / 324.

(End)

Example

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

Crossrefs

Column 2 of A280480.

Sequence in context: A152223 A152224 A238769 * A208790 A026112 A038155

Adjacent sequences: A280471 A280472 A280473 * A280475 A280476 A280477

Keyword

nonn

Author

R. H. Hardin, Jan 04 2017

Status

approved