A014082 Number of occurrences of '111' in binary expansion of n.
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
Offset: 0
Links
- Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
- Ralf Stephan, Some divide-and-conquer sequences ...
- Ralf Stephan, Table of generating functions
- Eric Weisstein's World of Mathematics, Digit Block
- Index entries for sequences related to binary expansion of n
Crossrefs
Programs
-
Haskell
import Data.List (tails, isPrefixOf) a014082 = sum . map (fromEnum . ([1,1,1] `isPrefixOf`)) . tails . a030308_row -- Reinhard Zumkeller, Jun 17 2012 -
Maple
See A014081. f:= proc(n) option remember; if n::even then procname(n/2) elif n mod 8 = 7 then 1 + procname((n-1)/2) else procname((n-1)/2) fi end proc: f(0):= 0: map(f, [$0..1000]); # Robert Israel, Sep 11 2015
-
Mathematica
f[n_] := Count[ Partition[ IntegerDigits[n, 2], 3, 1], {1, 1, 1}]; Table[f@n, {n, 0, 104}] (* 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 *) Table[SequenceCount[IntegerDigits[n,2],{1,1,1},Overlaps->True],{n,0,110}] (* Harvey P. Dale, Mar 05 2023 *) -
PARI
a(n) = hammingweight(bitand(n, bitand(n>>1, n>>2))); \\ Gheorghe Coserea, Aug 30 2015
Formula
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), where t=x^2^k. - Ralf Stephan, Sep 08 2003
Comments