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A279262 Number of n X 2 0..1 arrays with no element equal to a strict majority of its horizontal and vertical neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards. 3
0, 4, 10, 20, 38, 68, 120, 208, 358, 612, 1042, 1768, 2992, 5052, 8514, 14324, 24062, 40364, 67624, 113160, 189150, 315844, 526890, 878160, 1462368, 2433268, 4045690, 6721748, 11160278, 18517652, 30706392, 50888128, 84287062, 139531812 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Column 2 of A279268.

LINKS

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

FORMULA

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

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

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

a(n) = (1/25)*(2^(-n)*(-25*2^(2+n)+(50-6*sqrt(5))*(1-sqrt(5))^n + 50*(1+sqrt(5))^n + 6*sqrt(5)*(1+sqrt(5))^n - 5*(1-sqrt(5))^n*(1+sqrt(5))*n + 5*(-1+sqrt(5))*(1+sqrt(5))^n*n)).

(End)

EXAMPLE

Some solutions for n=4:

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

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

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

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

CROSSREFS

Cf. A279268.

Sequence in context: A038420 A008254 A301178 * A168673 A090164 A261635

Adjacent sequences:  A279259 A279260 A279261 * A279263 A279264 A279265

KEYWORD

nonn

AUTHOR

R. H. Hardin, Dec 08 2016

STATUS

approved

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Last modified July 29 06:21 EDT 2021. Contains 346340 sequences. (Running on oeis4.)