A280474 - OEIS

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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

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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