A243413 Number of Dyck paths of semilength n having exactly 1 occurrence of the consecutive steps UDUUDU (with U=(1,1), D=(1,-1)).

1, 5, 19, 70, 259, 962, 3585, 13399, 50201, 188481, 709001, 2671624, 10082895, 38107919, 144214978, 546413880, 2072553851, 7869081412, 29904874545, 113744129791, 432969825404, 1649313815911, 6287005845873, 23980562901849, 91523321091182, 349497990760012

Offset: 4

Author

Alois P. Heinz, Jun 04 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 4..550
• Vaclav Kotesovec, Recurrence (of order 10)

Crossrefs

Column k=1 of A243366.

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 = 0.0159763870992602878106411532836296... . - Vaclav Kotesovec, Jun 05 2014