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A014082
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Occurrences of '111' in binary expansion of n.
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12
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0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 2, 3, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 3, 4, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 2, 3, 0, 0, 0, 0, 0, 0, 0, 1, 0
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OFFSET
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0,16
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COMMENTS
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a(n) = A213629(n,7) for n > 6. - Reinhard Zumkeller, Jun 17 2012
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LINKS
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_Reinhard Zumkeller_, Table of n, a(n) for n = 0..10000
R. Stephan, Some divide-and-conquer sequences ...
R. Stephan, Table of generating functions
Eric Weisstein's World of Mathematics, Digit Block
Index entries for sequences related to binary expansion of n
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FORMULA
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a(2n) = a(n), a(2n+1) = a(n) + [n congruent to 3 mod 4]. - Ralf Stephan, Aug 21 2003
G.f.: 1/(1-x) * sum(k>=0, t^7(1-t)/(1-t^8), t=x^2^k). - Ralf Stephan, Sep 08 2003
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MAPLE
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See A014081.
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MATHEMATICA
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f[n_] := Count[ Partition[ IntegerDigits[n, 2], 3, 1], {1, 1, 1}]; Table[f@n, {n, 0, 104}] [From Robert G. Wilson v, Apr 02 2009]
a[0] = a[1] = 0; a[n_] := a[n] = If[EvenQ[n], a[n/2], a[(n - 1)/2] + Boole[Mod[(n - 1)/2, 4] == 3]]; Table[a[n], {n, 0, 104}] (* Jean-François Alcover, Oct 22 2012, after Ralf Stephan *)
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PROG
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(Haskell)
import Data.List (tails, isPrefixOf)
a014082 = sum . map (fromEnum . ([1, 1, 1] `isPrefixOf`)) .
tails . a030308_row
-- Reinhard Zumkeller, Jun 17 2012
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CROSSREFS
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Cf. A014081, A033264, A056974, A056975, A056976, A056977, A056978, A056979, A056980.
Sequence in context: A104488 A010103 A086078 * A102354 A193138 A162641
Adjacent sequences: A014079 A014080 A014081 * A014083 A014084 A014085
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KEYWORD
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nonn,easy
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AUTHOR
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Simon Plouffe
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STATUS
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approved
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