A243414 Number of Dyck paths of semilength n having exactly 2 (possibly overlapping) occurrences of the consecutive steps UDUUDU (with U=(1,1), D=(1,-1)).

1, 7, 34, 149, 627, 2584, 10529, 42606, 171563, 688255, 2752912, 10985005, 43747708, 173937910, 690592594, 2738547328, 10848121023, 42931655341, 169759128539, 670744883641, 2648384384709, 10450336782375, 41212385684767, 162440029038575, 639946101535124

Offset

6,2

Links

Alois P. Heinz, Table of n, a(n) for n = 6..550

Vaclav Kotesovec, Recurrence (of order 10)

Formula

a(n) ~ c * d^n * sqrt(n), where d = 3.8821590268628506747194368909643384... (same as for A243412) is the root of the equation d^8 - 2*d^7 - 10*d^6 + 12*d^5 - 5*d^4 - 2*d^3 - 5*d^2 - 8*d - 3 = 0, and c = 0.000227236615409194082906635273578... . - Vaclav Kotesovec, Jun 05 2014

Crossrefs

Column k=2 of A243366.

Sequence in context: A192803 A052161 A080960 * A335087 A213119 A099242

Adjacent sequences: A243411 A243412 A243413 * A243415 A243416 A243417

Keyword

nonn

Author

Alois P. Heinz, Jun 04 2014

Status

approved