OFFSET
0,16
COMMENTS
a(n) = A213629(n,7) for n > 6. - Reinhard Zumkeller, Jun 17 2012
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
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
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 *)
PROG
(Haskell)
import Data.List (tails, isPrefixOf)
a014082 = sum . map (fromEnum . ([1, 1, 1] `isPrefixOf`)) .
tails . a030308_row
-- Reinhard Zumkeller, Jun 17 2012
(PARI) a(n) = hammingweight(bitand(n, bitand(n>>1, n>>2))); \\ Gheorghe Coserea, Aug 30 2015
CROSSREFS
KEYWORD
nonn,easy,base
AUTHOR
STATUS
approved