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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: A229314 A055099 A335921 * A211304 A047065 A047008 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 December 7 10:56 EST 2023. Contains 367650 sequences. (Running on oeis4.)