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A163704 Number of n X 2 binary arrays with all 1s connected, a path of 1s from left column to lower right corner, and no 1 having more than two 1s adjacent. 1
1, 5, 11, 21, 38, 66, 112, 187, 309, 507, 828, 1348, 2190, 3553, 5759, 9329, 15106, 24454, 39580, 64055, 103657, 167735, 271416, 439176, 710618, 1149821, 1860467, 3010317, 4870814, 7881162, 12752008, 20633203, 33385245, 54018483, 87403764 (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) = 3*a(n-1) - 2*a(n-2) - a(n-3) + a(n-4) for n >= 6.

Conjectures from Colin Barker, Mar 25 2018: (Start)

G.f.: x*(1 + 2*x - 2*x^2 - x^3 + x^4) / ((1 - x)^2*(1 - x - x^2)).

a(n) = -4 + (2^(-n)*((1-sqrt(5))^n*(-5+2*sqrt(5)) + (1+sqrt(5))^n*(5+2*sqrt(5)))) / sqrt(5) - n for n>1.

(End)

EXAMPLE

All solutions for n=3:

  0 0   0 0   0 0   0 0   1 0   0 1   1 1   0 0   1 0   1 1   1 1

  0 0   0 1   1 0   1 1   1 0   0 1   1 0   1 1   1 1   0 1   0 1

  1 1   1 1   1 1   1 1   1 1   1 1   1 1   0 1   0 1   0 1   1 1

CROSSREFS

Cf. A023548. - R. J. Mathar, Aug 06 2009

Sequence in context: A298785 A163787 A166863 * A131898 A168642 A234597

Adjacent sequences:  A163701 A163702 A163703 * A163705 A163706 A163707

KEYWORD

nonn

AUTHOR

R. H. Hardin, Aug 03 2009

STATUS

approved

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Last modified April 5 00:43 EDT 2020. Contains 333238 sequences. (Running on oeis4.)