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A101402
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a(0)=0, a(1)=1; for n>=2, let k = smallest power of 2 that is >= n, then a(n) = a(k/2) + a(n-1-k/2).
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4
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0, 1, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 9, 9, 9, 9, 10, 10, 10, 11, 11, 12, 12, 13, 13, 13, 14, 14, 15, 15, 15, 15, 16, 16, 16, 17, 17, 18, 18, 18, 19, 19, 19, 20, 20, 21, 21, 21, 21, 22, 22, 22, 23, 23, 23, 24, 24, 24, 25, 25, 26, 26, 26, 26, 27, 27, 27
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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EXAMPLE
| a(2) = a(1) + a(0) = 1 = 1 + 0;
a(3) = a(2) + a(0) = 1 = 1 + 0;
a(4) = a(2) + a(1) = 2 = 1 + 1;
a(5) = a(4) + a(0) = 2 = 2 + 0;
a(6) = a(4) + a(1) = 3 = 2 + 1;
a(7) = a(4) + a(2) = 3 = 2 + 1;
a(8) = a(4) + a(3) = 3 = 2 + 1;
a(9) = a(8) + a(0) = 3 = 3 + 0;
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MATHEMATICA
| a[0] = 0; a[1] = 1; a[n_] := a[n] = Block[{p = 2^(Ceiling[Log[2, n]] - 1)}, a[p] + a[n - 1 - p]]; Table[ a@n, {n, 0, 100}] [From Robert G. Wilson (rgwv(AT)rgwv.com), Aug 17 2009]
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CROSSREFS
| Cf. A101403, A101404, A000045.
Sequence in context: A107320 A095186 A189631 * A156251 A116458 A093875
Adjacent sequences: A101399 A101400 A101401 * A101403 A101404 A101405
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KEYWORD
| easy,nonn
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AUTHOR
| Odimar Fabeny (aifab(AT)yahoo.com.br), Jan 16 2005
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EXTENSIONS
| Offset corrected by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 17 2009
More terms from Robert G. Wilson (rgwv(AT)rgwv.com), Aug 17 2009
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