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A163686 Number of n X 3 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, 5, 17, 39, 83, 175, 375, 807, 1732, 3690, 7805, 16441, 34605, 72893, 153653, 323917, 682654, 1438292, 3030059, 6383675, 13449863, 28338555, 59708355, 125801331, 265051912, 558439806, 1176585241, 2478972461, 5223002977, 11004454185 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

R. H. Hardin, Table of n, a(n) for n=1..56

FORMULA

Empirical: a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 2*a(n-4) - 6*a(n-5) + 6*a(n-6) - 2*a(n-7) - a(n-8) + a(n-9) for n>=13.

Empirical g.f.: x*(1 + 2*x^2 - 6*x^3 + 10*x^4 - 4*x^5 - 2*x^6 + 4*x^7 + 6*x^8 + 2*x^9 - 3*x^10 - 2*x^11) / ((1 - x)^2*(1 - x + x^2 + x^3)*(1 - 2*x - x^4)). - Colin Barker, Mar 25 2018

EXAMPLE

All solutions for n=3:

...1.0.0...1.0.0...1.0.0...1.0.0...1.1.0...1.1.0...1.1.1...1.1.1...1.1.0

...1.1.0...1.1.1...1.0.0...1.0.1...1.0.0...1.0.1...1.0.0...1.0.1...0.1.0

...0.1.1...0.0.1...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1...0.1.1

------

...1.1.0...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1...1.0.1...1.1.1

...0.1.1...0.0.1...0.0.1...1.0.1...1.0.1...1.0.1...1.0.1...0.0.1

...0.0.1...0.0.1...0.1.1...0.0.1...0.1.1...1.0.1...1.1.1...1.1.1

CROSSREFS

Sequence in context: A127744 A122734 A250413 * A147165 A147257 A146645

Adjacent sequences: A163683 A163684 A163685 * A163687 A163688 A163689

KEYWORD

nonn

AUTHOR

R. H. Hardin, Aug 03 2009

STATUS

approved

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Last modified January 31 14:31 EST 2023. Contains 359975 sequences. (Running on oeis4.)