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A038093
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Number of nodes in largest rooted identity tree of height n.
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15
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OFFSET
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0,2
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COMMENTS
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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
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LINKS
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FORMULA
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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
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EXAMPLE
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For n = 3, the n-th iteration of the von Neumann universe is V3 = {{}, {{}}, {{{}}}, {{},{{}}}}, which has a(3) = 11 pairs of braces.
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MAPLE
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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:
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MATHEMATICA
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Map[#[[1]]&, NestList[{(#[[1]]+1)*(2^#[[2]])/2+1, 2^#[[2]]}&, {1, 0}, 6]] (* Adam P. Goucher, Aug 18 2013 *)
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CROSSREFS
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Cf. A038082, A038083, A038084, A038085, A038086, A038087, A038088, A038089, A038090, A038091, A038092, A229403, A229404.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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