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A187721 Number of (n+1) X 2 binary arrays with no 2 X 2 subblock commuting with any of its horizontal and vertical 2 X 2 subblock neighbors. 1
16, 43, 130, 391, 1173, 3520, 10558, 31672, 95004, 284980, 854840, 2564222, 7691771, 23072626, 69209824, 207605302, 622743418, 1868012800, 5603386130, 16808201791, 50418736274, 151238603566, 453663001075, 1360830592810, 4082016602475 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Column 1 of A187729.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..200

FORMULA

Empirical: a(n) = 5*a(n-2) + 10*a(n-3) + 8*a(n-4) - 2*a(n-5) - 10*a(n-6) - 7*a(n-7) + 3*a(n-9) + a(n-10) for n>11.

Empirical g.f.: x*(16 + 43*x + 50*x^2 + 16*x^3 - 35*x^4 - 47*x^5 - 11*x^6 + 16*x^7 + 13*x^8 - 2*x^9 - 2*x^10) / (1 - 5*x^2 - 10*x^3 - 8*x^4 + 2*x^5 + 10*x^6 + 7*x^7 - 3*x^9 - x^10). - Colin Barker, Apr 25 2018

EXAMPLE

Some solutions for 3 X 2:

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

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

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

CROSSREFS

Cf. A187729.

Sequence in context: A187729 A088800 A316636 * A253397 A258554 A253326

Adjacent sequences:  A187718 A187719 A187720 * A187722 A187723 A187724

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 13 2011

STATUS

approved

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Last modified May 11 21:35 EDT 2021. Contains 343808 sequences. (Running on oeis4.)