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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
OFFSET
1,1
COMMENTS
Same recurrence for A163715.
Same recurrence for A163734.
LINKS
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Aug 03 2009
STATUS
approved