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A183721 1/12 the number of (n+1) X 2 0..5 arrays with every 2 X 2 subblock strictly increasing clockwise or counterclockwise with one decrease, and at least two adjacent blocks having the same increasing direction. 1
0, 1, 12, 87, 537, 3070, 16731, 88331, 455804, 2311983, 11571209, 57295330, 281223411, 1370286715, 6635743136, 31964799247, 153273890393, 732031932806, 3483896304443, 16529018119643, 78202676604548, 369073777749215 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Column 1 of A183729.

LINKS

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

FORMULA

Empirical: a(n) = 8*a(n-1) - 11*a(n-2) - 23*a(n-3) + 6*a(n-4) + 7*a(n-5) - 2*a(n-6).

Empirical g.f.: x^2*(1 + 2*x - x^2)^2 / ((1 + x)*(1 - 5*x + 2*x^2)*(1 - 4*x - 2*x^2 + x^3)). - Colin Barker, Apr 04 2018

EXAMPLE

All solutions with the first block increasing clockwise for 3 X 2:

..3..4....1..2....4..5....2..3....5..0....0..1

..2..5....0..3....3..0....1..4....4..1....5..2

..1..0....5..4....2..1....0..5....3..2....4..3

...

...R.......R.......R.......R.......R.......R...

...R.......R.......R.......R.......R.......R...

CROSSREFS

Cf. A183729.

Sequence in context: A091119 A243248 A046023 * A180797 A137207 A206765

Adjacent sequences:  A183718 A183719 A183720 * A183722 A183723 A183724

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jan 06 2011

STATUS

approved

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Last modified October 1 08:18 EDT 2022. Contains 357135 sequences. (Running on oeis4.)