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 A153362 Number of zig-zag paths from top to bottom of a rectangle of width 9 with n rows. 6
 9, 16, 30, 56, 106, 200, 380, 720, 1370, 2600, 4950, 9400, 17900, 34000, 64750, 123000, 234250, 445000, 847500, 1610000, 3066250, 5825000, 11093750, 21075000, 40137500, 76250000, 145218750, 275875000, 525406250, 998125000, 1900937500 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Number of words of length n using a 9 symbol alphabet where neighboring letters are neighbors in the alphabet. - Andrew Howroyd, Apr 17 2017 LINKS Table of n, a(n) for n=1..31. Joseph Myers, BMO 2008--2009 Round 1 Problem 1---Generalisation FORMULA Empirical G.f.: x*(9+16*x-15*x^2-24*x^3+x^4)/(1-5*x^2+5*x^4). [Colin Barker, Sep 02 2012] MATHEMATICA b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i == 0, Sum[b[n - 1, j, k], {j, 1, k}], If[i>1, b[n-1, i-1, k], 0] + If[i

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Last modified November 29 12:41 EST 2023. Contains 367445 sequences. (Running on oeis4.)