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Search: id:A086449
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| A086449 |
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a(0) = 1, a(2n+1) = a(n), a(2n) = a(n) + a(n-1) +...+ a(n-2^m) +...where a(n<0) = 0. |
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2
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| 1, 1, 2, 1, 4, 2, 4, 1, 8, 4, 8, 2, 12, 4, 8, 1, 18, 8, 16, 4, 26, 8, 16, 2, 34, 12, 24, 4, 36, 8, 16, 1, 48, 18, 36, 8, 60, 16, 32, 4, 80, 26, 52, 8, 78, 16, 32, 2, 104, 34, 68, 12, 110, 24, 48, 4, 136, 36, 72, 8, 108, 16, 32, 1, 154, 48, 96, 18, 160, 36, 72, 8
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Conjecture: all a(n) are even except a(2^k-1) = 1. Also a(2^k-2) = 2^(k-1). [For proof see link.]
Setting m=0 gives Stern-Brocot sequence (A002487).
a(n) = number of ways of writing n as a sum of powers of 2, where each power appears p times, with p itself a power of 2.
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LINKS
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Lambert Herrgesell, Proof of conjecture
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FORMULA
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G.f.: prod(k>=0, sum(l>=0, (x^(2^k))^(2^l))). [Corrected by Herb Wilf, May 31 2006]
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PROGRAM
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a(n)=local(k): if(n<1, n>=0, if(n%2==0, a(n/2)+sum(k=0, n, a((n-2^(k+1))/2)), a((n-1)/2)))
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CROSSREFS
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Cf. A086450.
Sequence in context: A121464 A090278 A082908 this_sequence A070556 A065295 A035685
Adjacent sequences: A086446 A086447 A086448 this_sequence A086450 A086451 A086452
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KEYWORD
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nonn,easy
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AUTHOR
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Ralf Stephan (ralf(AT)ark.in-berlin.de), Jul 20 2003
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