A083904 - OEIS

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A083904

G.f. 1/(1-x) * Sum_{k>=0} 3^k * x^2^(k+1)/(1+x^2^k).

0, 1, 0, 4, 3, 1, 0, 13, 12, 10, 9, 4, 3, 1, 0, 40, 39, 37, 36, 31, 30, 28, 27, 13, 12, 10, 9, 4, 3, 1, 0, 121, 120, 118, 117, 112, 111, 109, 108, 94, 93, 91, 90, 85, 84, 82, 81, 40, 39, 37, 36, 31, 30, 28, 27, 13, 12, 10, 9, 4, 3, 1, 0, 364, 363, 361, 360

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OFFSET

1,4

COMMENTS

Distance to next number of form 2^k-1, written down in binary, then interpreted as ternary. Thus the numbers have no 2 in ternary representation.

LINKS

Table of n, a(n) for n=1..67.

Ralf Stephan, Some divide-and-conquer sequences with (relatively) simple ordinary generating functions.

Ralf Stephan, Table of generating functions

FORMULA

a(1)=0, a(2n) = 3a(n)+1, a(2n+1) = 3a(n).

a(n) = (1/2)*(3^(floor(log_2(n))+1)-1) - A005836(n).