A036555 Hamming weight of 3n: number of 1's in binary expansion of 3n.

0, 2, 2, 2, 2, 4, 2, 3, 2, 4, 4, 2, 2, 4, 3, 4, 2, 4, 4, 4, 4, 6, 2, 3, 2, 4, 4, 3, 3, 5, 4, 5, 2, 4, 4, 4, 4, 6, 4, 5, 4, 6, 6, 2, 2, 4, 3, 4, 2, 4, 4, 4, 4, 6, 3, 4, 3, 5, 5, 4, 4, 6, 5, 6, 2, 4, 4, 4, 4, 6, 4, 5, 4, 6, 6, 4, 4, 6, 5, 6, 4, 6, 6, 6, 6, 8, 2, 3, 2, 4, 4, 3, 3, 5, 4, 5, 2, 4, 4

Offset

0,2

Comments

a(n) is also the largest integer such that 2^a(n) divides binomial(6n,3n)=A066802(n). - Benoit Cloitre, Mar 27 2002

a(n) = A000120(A008585(n)). - Reinhard Zumkeller, Nov 03 2010

a(A002450(n)) = 2*n.

Links

T. D. Noe, Table of n, a(n) for n = 0..1000

S. R. Finch, P. Sebah and Z.-Q. Bai, Odd Entries in Pascal's Trinomial Triangle (arXiv:0802.2654)

Philippe Flajolet, Peter Grabner, Peter Kirschenhofer, Helmut Prodinger and Robert F. Tichy, Mellin transforms and asymptotics: digital sums, Theoret. Comput. Sci. 123 (1994), 291-314.

Michael Gilleland, Some Self-Similar Integer Sequences

D. J. Newman, On the number of binary digits in a multiple of three, Proc. Amer. Math. Soc. 21 (1969) 719-721.

Maple

t1:=[];
for n from 0 to 100 do t2:=convert(3*n, base, 2); t3:=add(t2[i], i=1..nops(t2)); t1:=[op(t1), t3]; od:
t1;

Mathematica

Total/@IntegerDigits[3Range[0, 100], 2] (* Harvey P. Dale, Oct 03 2011 *)

Prog

(Haskell)
a036555 = a000120 . (* 3)  -- Reinhard Zumkeller, Sep 01 2013
(PARI) a(n) = hammingweight(3*n); \\ Michel Marcus, Mar 13 2014

Crossrefs

Cf. A036556, A036557, A099033, A190944.

Sequence in context: A061389 A366763 A138011 * A046927 A366563 A351411

Adjacent sequences: A036552 A036553 A036554 * A036556 A036557 A036558

Keyword

nonn,base,nice

Author

Dan Hoey

Extensions

Name edited by Michel Marcus, Mar 13 2014

Status

approved