The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A243872 Number of Dyck paths of semilength n having exactly 2 (possibly overlapping) occurrences of the consecutive steps UDUUUDDDUD (with U=(1,1), D=(1,-1)). 2
 1, 4, 16, 65, 263, 1077, 4419, 18132, 74368, 304778, 1247972, 5105477, 20867862, 85219608, 347724794, 1417697157, 5775652743, 23512922998, 95657223246, 388912046916, 1580241458120, 6417249216667, 26046042351889, 105661066012240, 428430870576913 (list; graph; refs; listen; history; text; internal format)
 OFFSET 9,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 9..400 Vaclav Kotesovec, Recurrence (of order 14) FORMULA a(n) ~ c * d^n * sqrt(n), where d = 3.992152919721564592666177480042427843835641823811... is the root of equation 1 - 2*d + d^2 - 6*d^5 + 2*d^6 - 4*d^9 + d^10 = 0, and c = 0.00000109315704269290466088403991068... . - Vaclav Kotesovec, Jul 16 2014 MAPLE b:= proc(x, y, t) option remember; `if`(y<0 or y>x, 0, `if`(x=0, 1,      series(b(x-1, y+1, [2, 2, 4, 5, 6, 2, 4, 2, 10, 2][t])+`if`(t=10,       z, 1)*b(x-1, y-1, [1, 3, 1, 3, 3, 7, 8, 9, 1, 3][t]), z, 3)))     end: a:= n-> coeff(b(2*n, 0, 1), z, 2): seq(a(n), n=9..40); MATHEMATICA b[x_, y_, t_] := b[x, y, t] = If[y<0 || y>x, 0, If[x==0, 1, Series[       b[x-1, y+1, {2, 2, 4, 5, 6, 2, 4, 2, 10, 2}[[t]]]+If[t==10, z, 1]*       b[x-1, y-1, {1, 3, 1, 3, 3, 7, 8, 9, 1, 3}[[t]]], {z, 0, 3}]]]; a[n_] := Coefficient[b[2n, 0, 1], z, 2]; a /@ Range[9, 40] (* Jean-François Alcover, Dec 27 2020, after Alois P. Heinz *) CROSSREFS Column k=2 of A243881. Column k=738 of A243828. Sequence in context: A175065 A033140 A181879 * A052927 A012781 A132820 Adjacent sequences:  A243869 A243870 A243871 * A243873 A243874 A243875 KEYWORD nonn AUTHOR Alois P. Heinz, Jun 13 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 8 16:43 EDT 2021. Contains 343666 sequences. (Running on oeis4.)