A163714 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

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, 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: A114113 A100056 A359147 * A333910 A307191 A234638

Adjacent sequences: A163711 A163712 A163713 * A163715 A163716 A163717

KEYWORD

nonn

AUTHOR

R. H. Hardin, Aug 03 2009

STATUS

approved