A061392 a(n) = a(floor(n/3)) + a(ceiling(n/3)) with a(0) = 0 and a(1) = 1.

0, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 6, 6, 6, 6, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 10, 10, 10, 10, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 14, 14, 14, 14, 15, 15, 16, 16, 16, 16, 16, 16, 16

Offset

0,4

Comments

Number of nonnegative integers < n having no 1 in their ternary representation. - Reinhard Zumkeller, Mar 23 2003; corrected by Henry Bottomley, Mar 24 2003

Links

Rémy Sigrist, Table of n, a(n) for n = 0..6561

Sam Northshield, Sums across Pascal’s triangle modulo 2, Congressus Numerantium, 200, pp. 35-52, 2010. [From Johannes W. Meijer, Jun 05 2011]

Wikipedia, Cantor function

Formula

a(n+1) + A081609(n) = n+1. - Reinhard Zumkeller, Mar 23 2003; corrected by Henry Bottomley, Mar 24 2003

From Johannes W. Meijer, Jun 05 2011: (Start)

a(3*n+1) = a(n+1) + a(n), a(3*n+2) = a(n+1) + a(n) and a(3*n+3) = 2*a(n+1), for n>=1, with a(0)=0, a(1)=1, a(2)=1 and a(3)=2. [Northshield]

G.f.: x*Product_{n>=0} (1 + x^(3^n) + 2*x^(2*3^n) + x^(3*3^n) + x^(4*3^n)). [Northshield] (End)

Apparently, for any n >= 0 and k such that n < 3^k, a(n) = 2^k * c(n / 3^k) where c is the Cantor function. - Rémy Sigrist, Jul 12 2019

Maple

A061392 := proc(n) option remember; local a : if n <=1 then n else A061392(floor(n/3)) + A061392(ceil(n/3)) fi: end: seq(A061392(n), n=0..87); # Johannes W. Meijer, Jun 05 2011

Crossrefs

k appears A061393(k) times.

Cf. A007089, A062756, A081608, A081609, A081611.

Essentially the partial sums of A088917.

Sequence in context: A308403 A073578 A087866 * A048273 A333535 A364678

Adjacent sequences: A061389 A061390 A061391 * A061393 A061394 A061395

Keyword

nonn,look

Author

Henry Bottomley, Apr 30 2001

Status

approved