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

Author

Antti Karttunen, Jan 02 2007

Keywords

• nonn

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.

Examples

			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.
		

Links

• 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.

Crossrefs

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

Formula

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

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