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

Offset: 1

Author

Ralf Stephan, Jun 18 2003

Keywords

• nonn
• easy

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

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

Crossrefs

Cf. A005823, A005836.

Programs

PARI

for(n=1, 100, l=ceil(log(n)/log(2)); t=polcoeff(1/(1-x)*sum(k=0, l, 3^k*(x^2^(k+1))/(1+x^2^k)) + O(x^(n+1)), n); print1(t", "))

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).