A038093 Number of nodes in largest rooted identity tree of height n.

1, 2, 4, 11, 97, 3211265

Offset

0,2

Comments

The next term is 19735 digits long, which is too large even for a b-file.

Also, the sequence gives the number of pairs of braces in the n-th iteration of the von Neumann universe. - Adam P. Goucher, Aug 18 2013

Links

Table of n, a(n) for n=0..5.

Adam P. Goucher, Article including the first five iterations of the von Neumann universe, "Complex Projective 4-Space" blog.

Index entries for sequences related to rooted trees

Formula

Recurrence relation: a(n+1) = (a(n) + 1)*(2^^n)/2 + 1 where 2^^n is Knuth's up-arrow notation. - Adam P. Goucher, Aug 18 2013

Example

For n = 3, the n-th iteration of the von Neumann universe is V3 = {{}, {{}}, {{{}}}, {{},{{}}}}, which has a(3) = 11 pairs of braces.

Maple

h:= (b, k)-> `if`(k=0, 1, b^h(b, k-1)):
a:= proc(n) option remember; `if`(n=0, 1,
       1+(1+a(n-1))/2*h(2, n-1))
    end:
seq(a(n), n=0..5);  # Alois P. Heinz, Aug 25 2017

Mathematica

Map[#[[1]]&, NestList[{(#[[1]]+1)*(2^#[[2]])/2+1, 2^#[[2]]}&, {1, 0}, 6]] (* Adam P. Goucher, Aug 18 2013 *)

Crossrefs

Cf. A038082, A038083, A038084, A038085, A038086, A038087, A038088, A038089, A038090, A038091, A038092, A229403, A229404.

Cf. A227819.

Sequence in context: A006894 A193565 A198864 * A057284 A156463 A227530

Adjacent sequences: A038090 A038091 A038092 * A038094 A038095 A038096

Keyword

nonn

Author

Christian G. Bower, Jan 04 1999

Extensions

a(6) from Adam P. Goucher, Aug 18 2013

Status

approved