A163724 - OEIS

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, 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