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A182093 Partial sums of A005590. 3
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified May 31 13:01 EDT 2020. Contains 334748 sequences. (Running on oeis4.)