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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). 3
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 (list; graph; refs; listen; history; text; internal format)
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 A154497

Adjacent sequences:  A243767 A243768 A243769 * A243771 A243772 A243773

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jun 10 2014

STATUS

approved

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Last modified February 23 09:32 EST 2018. Contains 299509 sequences. (Running on oeis4.)