A063573 First differences of A002065.

1, 2, 10, 170, 33490, 1133870930, 1285739648704587610, 1653126447166808568966775665261637370

Offset: 0

Author

N. J. A. Sloane, Sep 06 2001

Keywords

• nonn

Comments

Number of trees of height n generated by unary and binary composition. - Claude Lenormand (claude.lenormand(AT)free.fr), Sep 05 2001

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..11
• Samuele Giraudo, The combinator M and the Mockingbird lattice, arXiv:2204.03586 [math.CO], 2022.
• Samuele Giraudo, Mockingbird lattices, Séminaire Lotharingien de Combinatoire XX, Proceedings of the 34th Conf. on Formal Power, Series and Algebraic Combinatorics (Bangalore, India, 2022).
• Index entries for sequences of form a(n+1)=a(n)^2 + ...

Crossrefs

Cf. A002065.

Programs

Mathematica

a[0] = 1; Do[a[n] = a[n - 1]^2 + 2 a[n - 1] Sqrt[a[n - 1] - 1] + a[n - 1], {n, 7}]; Array[a, 8, 0] (* Michael De Vlieger, Apr 13 2022 *)

PARI

a(n)=if(n,my(k=a(n-1));k^2+2*k*sqrtint(k-1)+k,1) \\ Charles R Greathouse IV, Dec 29 2011

Formula

a(n) = a(n-1)^2 + 2 a(n-1) sqrt(a(n-1)-1) + a(n-1) for n > 0. [Charles R Greathouse IV, Dec 29 2011]