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, 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

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