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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
Adam P. Goucher, Article including the first five iterations of the von Neumann universe, "Complex Projective 4-Space" blog.
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. A227819.
Sequence in context: A006894 A193565 A198864 * A057284 A156463 A227530
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 May 18 14:56 EDT 2024. Contains 372641 sequences. (Running on oeis4.)