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Search: id:A051179
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| 1, 3, 15, 255, 65535, 4294967295, 18446744073709551615, 340282366920938463463374607431768211455, 115792089237316195423570985008687907853269984665640564039457584007913129639935
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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In a tree with binary nodes (0, 1 children only), the maximum number of unique child nodes at level n.
Number of binary trees (each vertex has 0, or 1 left, or 1 right, or 2 children) such that all leaves are at level n. Example: a(1) = 3 because we have (i) root with a left child, (ii) root with a right child, and (iii) root with two children. a(n)=A000215(n)-2. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 20 2004
The first 5 terms n (only) have the prpoerty that phi(n)=(n+1)/2, where phi(n)=A000010(n) is Euler's totient function. - Lekraj Beedassy (blekraj(AT)yahoo.com), Feb 12 2007
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REFERENCES
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M. Aigner and G. M. Ziegler, Proofs from The Book, Springer-Verlag, Berlin, 1999; see p. 4.
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LINKS
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For rate of growth see A. V. Aho and N. J. A. Sloane, Some doubly exponential sequences, Fib. Quart., 11 (1973), 429-437.
Index entries for sequences of form a(n+1)=a(n)^2 + ...
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FORMULA
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a(n) = (a(n-1) + 1)^2 - 1, a(0) = 1. [ or a(n) = a(n-1)(a(n-1) + 2) ].
1 = 2/3 + 4/15 + 16/255 + 256/65535...= Sum(0 through infinity) A001146(n)/a(n+1); with partial sums: 2/3, 14/15, 254/255, 65534/65535... - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 15 2003
a(n)=b(n-1) where b(1)=1, b(n) = prod(k=1, n-1, b(k)+2) - Benoit Cloitre (benoit7848c(AT)orange.fr), Sep 13 2003
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PROGRAM
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(PARI) a(n)=if(n<0, 0, 2^2^n-1)
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CROSSREFS
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Cf. A001146, A007018. Partial products of A000215.
a(n)=A000215(n)-2.
Adjacent sequences: A051176 A051177 A051178 this_sequence A051180 A051181 A051182
Sequence in context: A139289 A116518 A050474 this_sequence A122591 A120607 A013352
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Alan DeKok (aland(AT)ox.org)
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