

A153367


Number of zigzag paths from top to bottom of a rectangle of width 9 with 2n1 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
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OFFSET

1,1


LINKS



FORMULA

Empirical g.f.: x*(46*x)/(15*x+5*x^2).  Colin Barker, Jan 04 2012
a(n) = (2^(n)*((5sqrt(5))^n*(5+3*sqrt(5)) + (5+sqrt(5))^n*(5+3*sqrt(5)))) / (5*sqrt(5)) for n>0.
a(n) = 5*a(n1)  5*a(n2) for n>2.
(End)
Assuming Colin Barker's conjectures, a(2*n) = 2*5^(n1)*Lucas(2*(n+1)), a(2*n+1) = 2*5^n*Fibonacci(2*n+3).  Ehren Metcalfe, Apr 21 2018


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



