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A279865 Number of n X 1 0..2 arrays with no element unequal to a strict majority of its horizontal and vertical neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards. 3
0, 1, 0, 6, 6, 30, 54, 158, 342, 846, 1910, 4446, 10038, 22734, 50838, 113310, 250774, 552654, 1211958, 2647390, 5760630, 12492366, 27003990, 58202526, 125104086, 268228430, 573739254, 1224529758, 2608132022, 5544352206, 11764763670 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Column 1 of A279871.

LINKS

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

FORMULA

Empirical: a(n) = 3*a(n-1) +3*a(n-2) -11*a(n-3) -6*a(n-4) +12*a(n-5) +8*a(n-6).

Conjectures from Colin Barker, Feb 26 2018: (Start)

G.f.: x^2*(1 - x)^3 / ((1 + x)^3*(1 - 2*x)^3).

a(n) = (3*2^n*n^2 + 96*n^2 + 21*2^n*n + 2^(n+4) - 16) / 648 for n even.

a(n) = (3*2^n*n^2 - 96*n^2 + 21*2^n*n + 2^(n+4) + 16) / 648 for n odd.

(End)

EXAMPLE

All solutions for n=4:

..0. .0. .0. .0. .0. .0

..1. .0. .1. .0. .1. .1

..1. .1. .0. .1. .1. .2

..0. .2. .0. .0. .2. .2

CROSSREFS

Cf. A279871.

Sequence in context: A078637 A147799 A071021 * A321528 A074002 A359741

Adjacent sequences: A279862 A279863 A279864 * A279866 A279867 A279868

KEYWORD

nonn

AUTHOR

R. H. Hardin, Dec 21 2016

STATUS

approved

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Last modified January 30 09:51 EST 2023. Contains 359943 sequences. (Running on oeis4.)