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A153367
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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.
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5
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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
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1,1
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LINKS
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FORMULA
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Empirical g.f.: x*(4-6*x)/(1-5*x+5*x^2). - Colin Barker, Jan 04 2012
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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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