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A186456 Number of (n+1) X 4 binary arrays with every 2 X 2 subblock commuting with each of its horizontal and vertical 2 X 2 subblock neighbors. 1
42, 51, 111, 162, 270, 362, 590, 846, 1362, 1998, 3122, 4622, 7126, 10642, 16286, 24442, 37230, 56046, 85138, 128414, 194754, 294094, 445590, 673362, 1019630, 1541514, 2333390, 3528654, 5340178, 8076974, 12221906, 18487374, 27972502 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Column 3 of A186462.

LINKS

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

FORMULA

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

Empirical g.f.: x*(42 - 33*x + 9*x^2 + 24*x^3 - 36*x^4 - 16*x^5 + 19*x^6 - 7*x^7 + 16*x^8) / ((1 - x)*(1 - x - x^2 + x^3 - x^4)). - Colin Barker, Apr 17 2018

EXAMPLE

Some solutions for 3 X 4:

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

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

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

CROSSREFS

Cf. A186462.

Sequence in context: A249043 A063998 A255513 * A181647 A105346 A108119

Adjacent sequences:  A186453 A186454 A186455 * A186457 A186458 A186459

KEYWORD

nonn

AUTHOR

R. H. Hardin, Feb 22 2011

STATUS

approved

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Last modified August 3 13:22 EDT 2021. Contains 346438 sequences. (Running on oeis4.)