A217216 Dimension of algebraic generators of the algebra "Baxter" of order n.

0, 1, 1, 3, 11, 47, 221, 1113, 5903, 32607, 186143, 1092015, 6555515, 40137219, 249984481, 1580468321, 10125395007, 65639436955, 430048061915, 2844592155631, 18979693010495, 127641472658231, 864645413540671, 5896221199266519, 40455246946190079

Offset: 0

Author

N. J. A. Sloane, Oct 03 2012

Keywords

• nonn

Links

• G. Chatel and V. Pilaud, Cambrian Hopf Algebras, arXiv:1411.3704 [math.CO], 2014-2015.
• S. Giraudo, Algebraic and combinatorial structures on Baxter permutations, DMTCS proc. AO, FPSAC 2011 Rykjavik, (2011) 387-398
• S. Giraudo, Algebraic and combinatorial structures on pairs of twin binary trees, arXiv:1204.4776 [math.CO], 2012.
• S. Giraudo, Algebraic and combinatorial structures on pairs of twin binary trees, Journal of Algebra, Volume 360, 15 June 2012, Pages 115-157.

Crossrefs

Cf. A001181.

Programs

Mathematica

nmax = 25;
1-1/(1+Sum[HypergeometricPFQ[{-1-n, 1-n, -n}, {2, 3}, -1] x^n, {n, nmax}]) + O[x]^nmax // CoefficientList[#, x]& (* Jean-François Alcover, Sep 26 2018 *)

PARI

baxter(n) = sum(k=1, n, binomial(n+1, k-1) * binomial(n+1, k) * binomial(n+1, k+1) / (binomial(n+1, 1) * binomial(n+1, 2)));
lista(m) = {u = t + t*O(t^m); b = 1 + sum(n=1, m, baxter(n)*u^n); gfbc = 1 - 1/b; for (n=0, m, print1(polcoeff(gfbc, n, t), ", "));}
\\ Michel Marcus, Feb 16 2013

Formula

Giraudo gives a generating function.

a(n) ~ c * 8^n / n^4, where c = 4.21514033443045415032... - Vaclav Kotesovec, Apr 27 2024

Extensions

More terms from Michel Marcus, Feb 16 2013