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A163714 Number of n X 2 binary arrays with all 1s connected, a path of 1s from top row to bottom row, and no 1 having more than two 1s adjacent. 3
3, 7, 10, 16, 26, 42, 68, 110, 178, 288, 466, 754, 1220, 1974, 3194, 5168, 8362, 13530, 21892, 35422, 57314, 92736, 150050, 242786, 392836, 635622, 1028458, 1664080, 2692538, 4356618, 7049156, 11405774, 18454930, 29860704, 48315634, 78176338 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Same recurrence for A163695.

Same recurrence for A163733.

LINKS

R. H. Hardin, Table of n, a(n) for n=1..100

FORMULA

Empirical: a(n) = a(n-1) + a(n-2) for n>=5.

Conjectures from Colin Barker, Feb 22 2018: (Start)

G.f.: x*(1 + x)*(3 + x - x^2) / (1 - x - x^2).

a(n) = (2^(-n)*((1-sqrt(5))^n*(-3+sqrt(5)) + (1+sqrt(5))^n*(3+sqrt(5)))) / sqrt(5) for n>2.

(End)

EXAMPLE

All solutions for n=4:

...1.0...1.0...1.1...1.1...0.1...0.1...1.1...1.1...1.0...1.1...1.0...1.0...0.1

...1.0...1.0...1.0...1.0...0.1...0.1...0.1...0.1...1.0...1.0...1.1...1.1...0.1

...1.0...1.0...1.0...1.0...0.1...0.1...0.1...0.1...1.1...1.1...0.1...0.1...1.1

...1.0...1.1...1.0...1.1...0.1...1.1...0.1...1.1...0.1...0.1...0.1...1.1...1.0

------

...1.1...0.1...0.1

...0.1...1.1...1.1

...1.1...1.0...1.0

...1.0...1.0...1.1

CROSSREFS

Cf. A090991, A078642, A047992. - R. J. Mathar, Aug 06 2009

Sequence in context: A088636 A114113 A100056 * A333910 A307191 A234638

Adjacent sequences:  A163711 A163712 A163713 * A163715 A163716 A163717

KEYWORD

nonn

AUTHOR

R. H. Hardin, Aug 03 2009

STATUS

approved

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Last modified August 12 04:52 EDT 2022. Contains 356067 sequences. (Running on oeis4.)