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A038093 Number of nodes in largest rooted identity tree of height n. 15
1, 2, 4, 11, 97, 3211265 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 21 14:18 EST 2019. Contains 329371 sequences. (Running on oeis4.)