A243770 Number of Dyck paths of semilength n having exactly one occurrence of the consecutive step pattern given by the binary expansion of n, where 1=U=(1,1) and 0=D=(1,-1).

1, 1, 3, 11, 16, 57, 161, 927, 1997, 5539, 25638, 68850, 275765, 995088, 2784600, 19235059, 53549250, 177389053, 711629836, 2641203240, 7517769634, 31706388438, 147201204924, 455738363552, 1614252170849, 6020919907344, 23811404216400, 79787485940824

Offset

1,3

Links

Alois P. Heinz, Table of n, a(n) for n = 1..400

Example

a(1) = 1: (U)D.
a(2) = 1: U(UD)D.
a(3) = 3: UD(UU)DD, (UU)DDUD, (UU)DUDD.
a(4) = 11: UDUDU(UDD), UDU(UDD)UD, UDUUD(UDD), UDUU(UDD)D, U(UDD)UDUD, UUD(UDD)UD, UUDUD(UDD), UUDU(UDD)D, UU(UDD)DUD, UUUD(UDD)D, UUU(UDD)DD.

Crossrefs

Column k=1 of A243752.

Main diagonal of A243827.

Sequence in context: A198515 A035337 A029500 * A298701 A216911 A356074

Adjacent sequences: A243767 A243768 A243769 * A243771 A243772 A243773

Keyword

nonn

Author

Alois P. Heinz, Jun 10 2014

Status

approved