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A038093
Number of nodes in largest rooted identity tree of height n.
15
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
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 *)
KEYWORD
nonn
AUTHOR
Christian G. Bower, Jan 04 1999
EXTENSIONS
a(6) from Adam P. Goucher, Aug 18 2013
STATUS
approved