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A186475 Number of (n+1) X 3 0..3 arrays with every 2 X 2 subblock commuting with each of its horizontal and vertical 2 X 2 subblock neighbors. 1
205, 362, 701, 2049, 3442, 8223, 14492, 35081, 64280, 150785, 281928, 646756, 1233097, 2780008, 5384887, 11965960, 23479960, 51563275, 102260008, 222407905, 444938056, 960071644, 1934442193, 4147066744, 8404992631, 17923081288 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Column 2 of A186482.

LINKS

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

FORMULA

Empirical: a(n) = 2*a(n-1) + 2*a(n-2) - 6*a(n-3) + 6*a(n-4) - 3*a(n-5) for n>13.

Empirical g.f.: x*(205 - 48*x - 433*x^2 + 1153*x^3 - 1116*x^4 - 110*x^5 + 336*x^6 + 112*x^7- 33*x^8 + 3*x^9 + x^10 + 2*x^12) / ((1 - x)*(1 - x - 3*x^2 + 3*x^3 - 3*x^4)). - Colin Barker, Apr 18 2018

EXAMPLE

Some solutions for 5 X 3:

..2..0..2....2..1..0....0..0..3....1..2..0....3..1..0....0..2..1....0..3..0

..0..2..0....2..0..1....0..0..0....1..0..2....0..0..1....0..0..2....2..0..3

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

..0..1..0....3..0..2....2..0..0....0..0..1....3..0..0....3..0..0....0..0..2

..0..0..1....0..3..0....0..2..2....0..0..1....2..3..0....0..3..1....0..0..0

CROSSREFS

Cf. A186482.

Sequence in context: A116177 A191834 A042983 * A020170 A260471 A249703

Adjacent sequences:  A186472 A186473 A186474 * A186476 A186477 A186478

KEYWORD

nonn

AUTHOR

R. H. Hardin, Feb 22 2011

STATUS

approved

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Last modified June 5 09:58 EDT 2020. Contains 334840 sequences. (Running on oeis4.)