A102390 An odious count.

0, 1, 2, 0, 3, 0, 0, 4, 5, 0, 0, 6, 0, 7, 8, 0, 9, 0, 0, 10, 0, 11, 12, 0, 0, 13, 14, 0, 15, 0, 0, 16, 17, 0, 0, 18, 0, 19, 20, 0, 0, 21, 22, 0, 23, 0, 0, 24, 0, 25, 26, 0, 27, 0, 0, 28, 29, 0, 0, 30, 0, 31, 32, 0, 33, 0, 0, 34, 0, 35, 36, 0, 0, 37, 38, 0, 39, 0, 0, 40, 0, 41, 42, 0, 43, 0, 0, 44

Offset

0,3

Comments

Counting numbers appear at positions indexed by the odious numbers A000069, 0 otherwise.

Equals row sums of triangle A143466 starting with offset 1. - Gary W. Adamson, Aug 17 2008

Links

Amiram Eldar, Table of n, a(n) for n = 0..10000

Formula

a(n) = (1+floor(n/2))*(1-(-1)^A000120(n))/2.

a(n) = (1+floor(n/2))*(1-(-1)^A010060(n))/2.

A008619(n) = A102389(n) + a(n).

Mathematica

a[n_] := (1 + Floor[n/2])*(1 - (-1)^DigitCount[n, 2, 1])/2; Array[a, 100, 0] (* Amiram Eldar, Jul 22 2023 *)

Crossrefs

Cf. A000120, A008619, A010060, A102389, A143466.

Sequence in context: A141701 A167990 A071391 * A127640 A113303 A080089

Adjacent sequences: A102387 A102388 A102389 * A102391 A102392 A102393

Keyword

easy,nonn,base

Author

Paul Barry, Jan 06 2005

Status

approved