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A004065
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Define predecessors of n, P(n), to consist of numbers whose binary representation is obtained from that of n by replacing 10 by 01 or changing a final 1 to a 0; then a(0)=1, a(n) = Sum a(P(n)), n>0.
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3
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1, 1, 1, 1, 1, 2, 2, 2, 1, 3, 5, 7, 5, 12, 12, 12, 1, 4, 9, 16, 14, 42, 54, 66, 14, 56, 110, 176, 110, 286, 286, 286, 1, 5, 14, 30, 28, 100, 154, 220, 42, 198, 462, 858, 572, 1716, 2002, 2288, 42, 240, 702, 1560, 1274, 4550, 6552, 8840, 1274, 5824, 12376
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OFFSET
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0,6
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..8191
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EXAMPLE
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E.g. 201 = 11001001, so P(201) = {169, 197, 200}, a(201) = a(169) + a(197) + a(200).
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MAPLE
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P:= proc(n) local h, i, m, s, t;
t:= irem(n, 2, 'm');
s:= `if`(t=1, {n-1}, {});
for i from 0 while m>0 do h:= irem(m, 2, 'm');
if h=1 and t=0 then s:= s union {n- 2^i} fi; t:=h
od; s
end:
a:= proc(n) a(n):= `if`(n=0, 1, add(a(k), k=P(n))) end:
seq (a(n), n=0..80); # Alois P. Heinz, Jul 06 2012
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CROSSREFS
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A003121(n) = a(2^n-1).
Sequence in context: A103626 A026268 A089258 * A127496 A144393 A089400
Adjacent sequences: A004062 A004063 A004064 * A004066 A004067 A004068
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KEYWORD
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nonn
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AUTHOR
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David W. Wilson Jan 29 2000
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EXTENSIONS
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Entry revised by N. J. A. Sloane, Jun 14 2012
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STATUS
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approved
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