This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A126309 #12 Dec 25 2018 11:31:44 %S A126309 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, %T A126309 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, %U A126309 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 %N A126309 A014486-index for the Dyck path "compressed" from the n-th Dyck path encoded by A014486(n). %C A126309 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. %H A126309 Y. Poupard, <a href="http://www.numdam.org/item?id=BURO_1979__32__3_0">Sur les quasi-ponts</a>, Cahiers du Bureau Universitaire de Recherche Opérationelle, Cahier no. 32, Paris, 1979, pp. 3-20. %H A126309 J. Vaillé, <a href="http://dx.doi.org/10.1006/eujc.1996.0089">Une Bijection Explicative de Plusieurs Propriétés Remarquables des Ponts</a>, European J. Combin. 18 (1997), no. 1, 117-124. %F A126309 a(n) = A080300(A126308(A014486(n))). %F A126309 a(n) = A125985(A126310(A125986(n))). %e A126309 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: %e A126309 ....../\ %e A126309 .../\/..\ %e A126309 ../......\, %e A126309 which, after the peaks are removed, results %e A126309 .../\, %e A126309 ../..\ encoded by A014486(3), thus a(18)=3. %Y A126309 Cf. A014486, A080300, A125985, A125986, A126308, A126310. %K A126309 nonn %O A126309 0,9 %A A126309 _Antti Karttunen_, Jan 02 2007