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A069361 Number of 3 X n binary arrays with a path of adjacent 1's from top row to bottom row. 92
1, 17, 197, 1985, 18621, 167337, 1461797, 12519345, 105683341, 882516857, 7308428597, 60131384705, 492202181661, 4012347269577, 32599584662597, 264152863210065, 2135714594033581, 17236446198921497, 138901692341235797, 1117982939085627425, 8989229069675479101 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (15,-58,16).

FORMULA

G.f.: x*(1+2*x)/((1-8*x)*(2*x^2-7*x+1)). - Vladeta Jovovic, Jul 02 2003

From Maksym Voznyy (voznyy(AT)mail.ru), Jul 25 2008: (Start)

a(n) = 15*a(n-1) - 58*a(n-2) + 16*a(n-3), where a(1)=1, a(2)=17, a(3)=197;

a(n) = 8^n + 1/sqrt(41)*4^(n+1)*((7+sqrt(41))^(-(n+1)) - (7-sqrt(41))^(-(n+1))). (End)

a(n) = 8^n - A186446(n). - R. J. Mathar, Jan 27 2020

MATHEMATICA

CoefficientList[Series[(-2 z - 1)/(16 z^3 - 58 z^2 + 15 z - 1), {z, 0, 100}], z] (* Vladimir Joseph Stephan Orlovsky, Jun 24 2011 *)

PROG

(PARI) x='x+O('x^30); Vec(x*(1+2*x)/((1-8*x)*(2*x^2-7*x+1))) \\ G. C. Greubel, Apr 22 2018

CROSSREFS

Cf. 1 X n A000225, 2 X n A005061, n X 2 A001333, vertical path of 1 A069361-A069395, vertical paths of 0+1 A069396-A069416, vertical path of 1 not 0 A069417-A069428, no vertical paths A069429-A069447, no horizontal or vertical paths A069448-A069452.

Sequence in context: A238672 A018250 A021184 * A177135 A130817 A055432

Adjacent sequences:  A069358 A069359 A069360 * A069362 A069363 A069364

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 22 2002

STATUS

approved

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Last modified February 26 11:49 EST 2020. Contains 332279 sequences. (Running on oeis4.)