The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A344432 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A344432

a(n) = Sum_{k=1..n} mu(k) * 2^(n - k).
(history; published version)

#22 by Alois P. Heinz at Wed May 19 16:48:24 EDT 2021

STATUS

proposed

approved

#21 by Vaclav Kotesovec at Wed May 19 12:59:33 EDT 2021

STATUS

editing

proposed

#20 by Vaclav Kotesovec at Wed May 19 12:59:26 EDT 2021

FORMULA

a(n) ~ A238270 * 2^n. - Vaclav Kotesovec, May 19 2021

#19 by Vaclav Kotesovec at Wed May 19 12:57:24 EDT 2021

CROSSREFS

Cf. A127513, A238270, A292524, A343425, A344433.

STATUS

proposed

editing

#18 by Seiichi Manyama at Wed May 19 11:59:38 EDT 2021

STATUS

editing

proposed

#17 by Seiichi Manyama at Wed May 19 11:55:17 EDT 2021

NAME

a(n) = Sum_{k=1 .. n} mu(k) * 2^(n - k).

#16 by Seiichi Manyama at Wed May 19 11:54:07 EDT 2021

LINKS

Seiichi Manyama, <a href="/A344432/b344432.txt">Table of n, a(n) for n = 0..1000</a>

#15 by Seiichi Manyama at Wed May 19 11:33:55 EDT 2021

FORMULA

a(n) = 2 * a(n-1) + mu(n) for n > 0.

PROG

(PARI) my(N=40, x='x+O('x^N)); concat(0, Vec(sum(k=1, N, moebius(k)*x^k)/(1-2*x)))

#14 by Seiichi Manyama at Wed May 19 11:33:19 EDT 2021

DATA

0, 1, 1, 1, 2, 3, 7, 13, 26, 52, 105, 209, 418, 835, 1671, 3343, 6686, 13371, 26742, 53483, 106966, 213933, 427867, 855733, 1711466, 3422932, 6845865, 13691730, 27383460, 54766919, 109533837, 219067673, 438135346, 876270693, 1752541387, 3505082775, 7010165550

OFFSET

1,4

0,5

FORMULA

a(n) = 2 * a(n-1) + mu(n) for n>0.

PROG

(PARI) a(n) = if(n==0, 0, 2*a(n-1)+moebius(n));

STATUS

approved

editing

#13 by Susanna Cuyler at Wed May 19 10:23:59 EDT 2021

STATUS

proposed

approved