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A163696 Number of n X 3 binary arrays with all 1s connected, a path of 1s from top row to lower right corner, and no 1 having more than two 1s adjacent. 3
3, 11, 28, 63, 138, 298, 642, 1371, 2908, 6146, 12970, 27351, 57654, 121502, 256026, 539459, 1136632, 2394830, 5045754, 10631039, 22398786, 47192482, 99430802, 209492731, 441384340, 929961258, 1959353418, 4128199671, 8697783790 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Same recurrence for A163715.

Same recurrence for A163734.

LINKS

R. H. Hardin, Table of n, a(n) for n=1..57

FORMULA

Empirical: a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3) + a(n-4) - 2*a(n-5) + a(n-6) for n>=10.

Empirical g.f.: x*(3 - x - x^2 + x^4 + 5*x^6 - x^7 - 2*x^8) / ((1 - x)^2*(1 - 2*x - x^4)). - Colin Barker, Feb 22 2018

EXAMPLE

All solutions for n=2:

...0.0.1...0.1.1...0.0.1...0.1.1...1.1.1...0.0.1...1.1.1...0.1.0...1.1.0

...0.0.1...0.0.1...0.1.1...0.1.1...0.0.1...1.1.1...1.0.1...0.1.1...0.1.1

------

...1.0.0...1.0.1

...1.1.1...1.1.1

CROSSREFS

Sequence in context: A119074 A211810 A182260 * A092781 A332669 A302509

Adjacent sequences: A163693 A163694 A163695 * A163697 A163698 A163699

KEYWORD

nonn

AUTHOR

R. H. Hardin, Aug 03 2009

STATUS

approved

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Last modified February 8 15:14 EST 2023. Contains 360149 sequences. (Running on oeis4.)