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A163695 Number of n X 2 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. 4
2, 5, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, 1364, 2207, 3571, 5778, 9349, 15127, 24476, 39603, 64079, 103682, 167761, 271443, 439204, 710647, 1149851, 1860498, 3010349, 4870847, 7881196, 12752043, 20633239, 33385282, 54018521, 87403803 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (1,1).

FORMULA

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

[The Transfer Matrix Method provides this recurrence. - R. J. Mathar, Aug 02 2017]

From Colin Barker, Feb 20 2018: (Start)

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

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

(End)

EXAMPLE

All solutions for n=4:

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

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

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

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

PROG

(PARI) Vec(x*(2 - x)*(1 + x)^2 / (1 - x - x^2) + O(x^60)) \\ Colin Barker, Feb 20 2018

CROSSREFS

It appears that A163714 and A163733 have the same recurrence as this sequence.

Cf. A288219.

Sequence in context: A338339 A224320 A247052 * A134641 A162491 A152216

Adjacent sequences: A163692 A163693 A163694 * A163696 A163697 A163698

KEYWORD

nonn,easy

AUTHOR

R. H. Hardin, Aug 03 2009

STATUS

approved

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Last modified January 29 07:25 EST 2023. Contains 359915 sequences. (Running on oeis4.)