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 A210737 Number of Dyck n-paths all of whose ascents have prime lengths. 4
 1, 0, 1, 1, 2, 6, 8, 29, 50, 141, 327, 771, 2047, 4746, 12644, 30941, 79886, 204885, 522242, 1365056, 3505825, 9185742, 23907116, 62636476, 164624803, 432540010, 1142827935, 3017208675, 7996379870, 21211540268, 56369770281, 150086840133, 400009010758 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..700 FORMULA a(n) ~ c * d^n / n^(3/2), where d = 2.7925684676903082567..., c = 0.4016264581712556... . - Vaclav Kotesovec, Sep 02 2014 EXAMPLE a(0) = 1: the empty path. a(1) = 0. a(2) = 1: UUDD. a(3) = 1: UUUDDD. a(4) = 2: UUDDUUDD, UUDUUDDD. a(5) = 6: UUDDUUUDDD, UUDUUUDDDD, UUUDDDUUDD, UUUDDUUDDD, UUUDUUDDDD, UUUUUDDDDD. a(6) = 8: UUDDUUDDUUDD, UUDDUUDUUDDD, UUDUUDDDUUDD, UUDUUDDUUDDD, UUDUUDUUDDDD, UUUDDDUUUDDD, UUUDDUUUDDDD, UUUDUUUDDDDD. MAPLE with(numtheory): b:= proc(x, y, u) option remember;       `if`(x<0 or  y b(n, n, true): seq(a(n), n=0..40); MATHEMATICA b[x_, y_, u_] := b[x, y, u] = If[x<0 || y

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Last modified October 14 03:58 EDT 2019. Contains 327995 sequences. (Running on oeis4.)