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A163724 Number of n X 3 binary arrays with all 1s connected, a path of 1s from left column to right column, and no 1 having more than two 1s adjacent. 1
1, 10, 48, 163, 463, 1186, 2854, 6597, 14839, 32754, 71352, 154007, 330251, 704902, 1499542, 3182221, 6741015, 14260846, 30139532, 63651099, 134348403, 283449142, 597830318, 1260590809, 2657595859, 5601979130, 11807185052, 24883686939 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

R. H. Hardin, Table of n, a(n) for n=1..49

FORMULA

Empirical: a(n) = 7*a(n-1) - 19*a(n-2) + 24*a(n-3) - 10*a(n-4) - 10*a(n-5) + 16*a(n-6) - 8*a(n-7) - a(n-8) + 3*a(n-9) - a(n-10) for n>=12.

Empirical g.f.: x*(1 + 3*x - 3*x^2 - 7*x^3 + 4*x^4 + x^6 - x^7 - 5*x^8 + x^9 + 2*x^10) / ((1 - x)^4*(1 - x - x^2)*(1 - 2*x - x^4)). - Colin Barker, Mar 25 2018

EXAMPLE

All solutions for n=2:

...1.1.1...1.1.1...1.1.1...1.1.1...0.0.0...0.0.1...1.0.0...1.0.1...1.1.0

...0.0.0...0.0.1...1.0.0...1.0.1...1.1.1...1.1.1...1.1.1...1.1.1...0.1.1

------

...0.1.1

...1.1.0

CROSSREFS

Sequence in context: A195023 A353620 A277229 * A271638 A238916 A084857

Adjacent sequences:  A163721 A163722 A163723 * A163725 A163726 A163727

KEYWORD

nonn

AUTHOR

R. H. Hardin, Aug 03 2009

STATUS

approved

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Last modified June 28 10:20 EDT 2022. Contains 354903 sequences. (Running on oeis4.)