A126309 A014486-index for the Dyck path "compressed" from the n-th Dyck path encoded by A014486(n).

0, 0, 0, 1, 0, 1, 1, 1, 3, 0, 1, 1, 1, 3, 1, 2, 1, 1, 3, 3, 3, 3, 8, 0, 1, 1, 1, 3, 1, 2, 1, 1, 3, 3, 3, 3, 8, 1, 2, 2, 2, 5, 1, 2, 1, 1, 3, 3, 3, 3, 8, 3, 6, 3, 3, 7, 3, 3, 3, 8, 8, 8, 8, 8, 22, 0, 1, 1, 1, 3, 1, 2, 1, 1, 3, 3, 3, 3, 8, 1, 2, 2, 2, 5, 1, 2, 1, 1, 3, 3, 3, 3, 8, 3, 6, 3, 3, 7, 3, 3, 3, 8

Offset

0,9

Comments

According to Vaillé, the concept of "compression d'un pont" was introduced by Poupard, in "Sur les quasi-ponts" paper. In effect, the operation removes all the peaks /\ from the Dyck path.

Links

Table of n, a(n) for n=0..101.

Y. Poupard, Sur les quasi-ponts, Cahiers du Bureau Universitaire de Recherche Opérationelle, Cahier no. 32, Paris, 1979, pp. 3-20.

J. Vaillé, Une Bijection Explicative de Plusieurs Propriétés Remarquables des Ponts, European J. Combin. 18 (1997), no. 1, 117-124.

Formula

a(n) = A080300(A126308(A014486(n))).

a(n) = A125985(A126310(A125986(n))).

Example

A014486(4) encodes the Dyck path /\/\/\, of which, when all the peaks are removed, nothing remains, thus a(4)=0. A014486(18) encodes the Dyck path:
....../\
.../\/..\
../......\,
which, after the peaks are removed, results
.../\,
../..\ encoded by A014486(3), thus a(18)=3.

Crossrefs

Cf. A014486, A080300, A125985, A125986, A126308, A126310.

Sequence in context: A181875 A051908 A056614 * A338940 A048838 A181872

Adjacent sequences: A126306 A126307 A126308 * A126310 A126311 A126312

Keyword

nonn

Author

Antti Karttunen, Jan 02 2007

Status

approved