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A153367 Number of zig-zag paths from top to bottom of a rectangle of width 9 with 2n-1 rows whose color is not that of the top right corner. 5
4, 14, 50, 180, 650, 2350, 8500, 30750, 111250, 402500, 1456250, 5268750, 19062500, 68968750, 249531250, 902812500, 3266406250, 11817968750, 42757812500, 154699218750, 559707031250, 2025039062500, 7326660156250, 26508105468750 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..24.

Joseph Myers, BMO 2008--2009 Round 1 Problem 1---Generalisation

FORMULA

Empirical g.f.: x*(4-6*x)/(1-5*x+5*x^2). - Colin Barker, Jan 04 2012

Conjectures from Colin Barker, Feb 11 2018: (Start)

a(n) = (2^(-n)*((5-sqrt(5))^n*(-5+3*sqrt(5)) + (5+sqrt(5))^n*(5+3*sqrt(5)))) / (5*sqrt(5)) for n>0.

a(n) = 5*a(n-1) - 5*a(n-2) for n>2.

(End)

Assuming Colin Barker's conjectures, a(2*n) = 2*5^(n-1)*Lucas(2*(n+1)), a(2*n+1) = 2*5^n*Fibonacci(2*n+3). - Ehren Metcalfe, Apr 21 2018

CROSSREFS

Cf. A153362, A153363, A153364, A153365, A153366.

Sequence in context: A120747 A229314 A055099 * A211304 A047008 A047065

Adjacent sequences:  A153364 A153365 A153366 * A153368 A153369 A153370

KEYWORD

nonn,easy

AUTHOR

Joseph Myers, Dec 24 2008

STATUS

approved

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Last modified January 26 20:33 EST 2020. Contains 331288 sequences. (Running on oeis4.)