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

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 *)

Prog

(PARI) for(n=1, 120, l=ceil(log(n)/log(2)); t=polcoeff(1/(1-x)*sum(k=0, l, (x^2^(k+2))/(1+x^2^k)) + O(x^(n+1)), n); print1(t", "))

Crossrefs

Cf. A000120, A023416, A079944, A080791.

Sequence in context: A060826 A078134 A282380 * A029369 A255315 A125072

Adjacent sequences: A083658 A083659 A083660 * A083662 A083663 A083664

Keyword

nonn,easy

Author

Ralf Stephan, Jun 14 2003

Status

approved