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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 22 06:54 EDT 2022. Contains 353933 sequences. (Running on oeis4.)