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A269012 Number of 2 X n binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once. 1
0, 4, 8, 36, 88, 272, 696, 1900, 4856, 12588, 31792, 80288, 200304, 498004, 1229672, 3024948, 7407496, 18079664, 43980072, 106688956, 258132824, 623113020, 1500935776, 3608439104, 8659683552, 20747930788, 49635222728, 118576046148 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

FORMULA

Empirical: a(n) = 2*a(n-1) + 5*a(n-2) - 6*a(n-3) - 9*a(n-4).

Conjectures from Colin Barker, Jan 18 2019: (Start)

G.f.: 4*x^2 / (1 - x - 3*x^2)^2.

a(n) = 4*(-((1/2)*(1+sqrt(13)))^n*(sqrt(13)-13*n) + ((1/2)*(1-sqrt(13)))^n*(sqrt(13)+13*n)) / 169.

(End)

EXAMPLE

Some solutions for n=4:

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

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

CROSSREFS

Row 2 of A269011.

Sequence in context: A044829 A338086 A033001 * A149110 A149111 A149112

Adjacent sequences:  A269009 A269010 A269011 * A269013 A269014 A269015

KEYWORD

nonn

AUTHOR

R. H. Hardin, Feb 17 2016

STATUS

approved

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Last modified October 21 06:56 EDT 2021. Contains 348144 sequences. (Running on oeis4.)