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A163685 Number of nX2 binary arrays with all 1s connected, a path of 1s from upper left corner to lower right corner, and no 1 having more than two 1s adjacent 1
1, 3, 5, 8, 13, 20, 32, 52, 85, 138, 223, 360, 582, 942, 1525, 2468, 3993, 6460, 10452, 16912, 27365, 44278, 71643, 115920, 187562, 303482, 491045, 794528, 1285573, 2080100, 3365672, 5445772, 8811445, 14257218, 23068663, 37325880, 60394542 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

FORMULA

Empirical: a(n)=2*a(n-1)-a(n-2)+a(n-4) for n>=7

Empirical: G.f.: x*(-x^3-x^4+x^5-x-1)/((x^2-x+1)*(x^2+x-1)). a(n)=5*A000045(n)/2-A010892(n+1)/2, n>2. [From R. J. Mathar, Aug 11 2009]

EXAMPLE

All solutions for n=5

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

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

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

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

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

CROSSREFS

Sequence in context: A265067 A265068 A227547 * A080614 A079122 A265069

Adjacent sequences: A163682 A163683 A163684 * A163686 A163687 A163688

KEYWORD

nonn

AUTHOR

R. H. Hardin Aug 03 2009

STATUS

approved

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Last modified February 3 23:01 EST 2023. Contains 360045 sequences. (Running on oeis4.)