A182093 Partial sums of A005590.

0, 1, 2, 2, 3, 2, 2, 3, 4, 2, 1, 2, 2, 3, 4, 4, 5, 2, 0, 1, 0, 2, 3, 2, 2, 3, 4, 4, 5, 4, 4, 5, 6, 2, -1, 0, -2, 1, 2, 0, -1, 2, 4, 3, 4, 2, 1, 2, 2, 3, 4, 4, 5, 4, 4, 5, 6, 4, 3, 4, 4, 5, 6, 6, 7, 2, -2, -1, -4, 0, 1, -2, -4, 1, 4, 2, 3, 0, -2, -1, -2, 2, 5

Offset

0,3

Comments

a(n+1) = a(n) + A005590(n+1).

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Formula

a(2^n) = n + 1.

G.f.: (x/(1 - x))*Product_{k>=0} (1 + x^(2^k) - x^(2^(k+1))). - Ilya Gutkovskiy, Feb 27 2017

Mathematica

a[0] = 0; a[1] = 1; a[n_] := a[n] = If[OddQ@ n, a[(n - 1)/2 + 1] - a[(n - 1)/2], a[n/2]]; Accumulate@ Table[a@ n, {n, 0, 104}] (* after Jean-François Alcover at A005590, or *)
Table[SeriesCoefficient[(x/(1 - x)) Product[(1 + x^(2^k) - x^(2^(k + 1))), {k, 0, n}], {x, 0, n}], {n, 0, 70}] (* Michael De Vlieger, Feb 27 2017 *)

Prog

(Haskell)
a182093 n = a182093_list !! n
a182093_list = scanl1 (+) a005590_list

Crossrefs

Cf. A005590.

Sequence in context: A306991 A239585 A321788 * A254618 A268672 A054483

Adjacent sequences: A182090 A182091 A182092 * A182094 A182095 A182096

Keyword

sign,look

Author

Reinhard Zumkeller, Apr 11 2012

Status

approved