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

1, 2, 4, 11, 97, 3211265

Offset: 0

Author

Christian G. Bower, Jan 04 1999

Keywords

• nonn

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

Examples

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

Links

• 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

Crossrefs

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

Cf. A227819.

Programs

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 *)

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

Extensions

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