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A186465 Number of (n+1) X 3 0..2 arrays with every 2 X 2 subblock commuting with each of its horizontal and vertical 2 X 2 subblock neighbors. 1
83, 129, 243, 562, 903, 1754, 2937, 5790, 9993, 19236, 33546, 63642, 112278, 210972, 375366, 700068, 1253442, 2324820, 4182330, 7725252, 13947186, 25682700, 46491258, 85412820, 154924338, 284132892, 516138474, 945381252, 1719241122 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Column 2 of A186472.

LINKS

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

FORMULA

Empirical: a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + 4*a(n-4) - 2*a(n-5) for n>11.

Empirical g.f.: x*(83 - 37*x - 98*x^2 + 279*x^3 - 280*x^4 + 8*x^5 + 60*x^6 + 12*x^7 + 4*x^8 - 2*x^9 + x^10) / ((1 - x)*(1 - x - 2*x^2 + 2*x^3 - 2*x^4)). - Colin Barker, Apr 18 2018

EXAMPLE

Some solutions for 5 X 3:

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

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

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

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

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

CROSSREFS

Cf. A186472.

Sequence in context: A261087 A140771 A142309 * A142409 A210527 A140038

Adjacent sequences:  A186462 A186463 A186464 * A186466 A186467 A186468

KEYWORD

nonn

AUTHOR

R. H. Hardin, Feb 22 2011

STATUS

approved

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Last modified July 30 12:39 EDT 2021. Contains 346359 sequences. (Running on oeis4.)