A083661 - OEIS

A083661

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

0, 0, 0, 1, 0, 1, 0, 2, 1, 1, 0, 2, 1, 1, 0, 3, 2, 2, 1, 2, 1, 1, 0, 3, 2, 2, 1, 2, 1, 1, 0, 4, 3, 3, 2, 3, 2, 2, 1, 3, 2, 2, 1, 2, 1, 1, 0, 4, 3, 3, 2, 3, 2, 2, 1, 3, 2, 2, 1, 2, 1, 1, 0, 5, 4, 4, 3, 4, 3, 3, 2, 4, 3, 3, 2, 3, 2, 2, 1, 4, 3, 3, 2, 3, 2, 2, 1, 3, 2, 2, 1, 2, 1

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,8

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

Ralf Stephan, Some divide-and-conquer sequences with (relatively) simple ordinary generating functions, 2004.

Ralf Stephan, Table of generating functions.

FORMULA

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

a(n) = A080791(n) + A079944(n-2) - 1.

MATHEMATICA

a[n_] := DigitCount[n, 2, 0] + IntegerDigits[n, 2][[2]] - 1; a[1] = 0; Array[a, 100] (* Amiram Eldar, Jul 16 2023 *)