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A036555 Hamming weight of 3n: number of 1's in binary expansion of 3n. 7
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 (list; graph; refs; listen; history; text; internal format)
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: A322483 A061389 A138011 * A046927 A084718 A154851

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

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Last modified April 16 05:26 EDT 2021. Contains 343030 sequences. (Running on oeis4.)