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A091311 Partial sums of 3^A007814(n). 0
0, 1, 4, 5, 14, 15, 18, 19, 46, 47, 50, 51, 60, 61, 64, 65, 146, 147, 150, 151, 160, 161, 164, 165, 192, 193, 196, 197, 206, 207, 210, 211, 454, 455, 458, 459, 468, 469, 472, 473, 500, 501, 504, 505, 514, 515, 518, 519, 600, 601, 604, 605, 614, 615, 618, 619 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..55.

FORMULA

Recurrence: a(2n) = 3a(n) + n, a(2n+1) = 3a(n) + n + 1.

G.f.: 1/(1-x) * sum(k>=0, 3^k*t/(1-t^2), t=x^2^k).

PROG

(PARI) a(n)=sum(k=1, n, 3^valuation(n, 2))

(PARI) a(n)=if(n<1, 0, if(n%2==0, 3*a(n/2)+n/2, 3*a((n-1)/2)+(n+1)/2))

CROSSREFS

First differences are A061393(n)-1.

Equals 2*A005836(n) - n.

Sequence in context: A239615 A195747 A238315 * A008540 A290810 A000867

Adjacent sequences:  A091308 A091309 A091310 * A091312 A091313 A091314

KEYWORD

nonn,easy

AUTHOR

Ralf Stephan, Feb 24 2004

STATUS

approved

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Last modified September 15 14:04 EDT 2019. Contains 327078 sequences. (Running on oeis4.)