A344432 a(n) = Sum_{k=1..n} mu(k) * 2^(n - k).
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: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..1000
Programs
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Mathematica
a[n_] := Sum[MoebiusMu[k] * 2^(n-k), {k,1,n}]; Array[a, 40] (* Amiram Eldar, May 19 2021 *) -
PARI
a(n) = sum(k=1, n, moebius(k)*2^(n-k));
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PARI
my(N=40, x='x+O('x^N)); concat(0, Vec(sum(k=1, N, moebius(k)*x^k)/(1-2*x))) -
PARI
a(n) = if(n==0, 0, 2*a(n-1)+moebius(n));
Formula
G.f.: (Sum_{k>=1} mu(k) * x^k) / (1 - 2*x).
a(n) = 2 * a(n-1) + mu(n) for n > 0.
a(n) ~ A238270 * 2^n. - Vaclav Kotesovec, May 19 2021