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.

4, 14, 50, 180, 650, 2350, 8500, 30750, 111250, 402500, 1456250, 5268750, 19062500, 68968750, 249531250, 902812500, 3266406250, 11817968750, 42757812500, 154699218750, 559707031250, 2025039062500, 7326660156250, 26508105468750

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: A055099 A335921 A372874 * A211304 A047065 A047008

Adjacent sequences: A153364 A153365 A153366 * A153368 A153369 A153370

Keyword

nonn,easy

Author

Joseph Myers, Dec 24 2008

Status

approved