A195133 Partial sums of A194577.

1, 2, 0, 4, 2, -2, -4, 8, 10, 6, 4, -12, -14, -18, -12, 24, 22, 30, 28, 12, 18, 14, 12, -44, -42, -46, -48, -64, -66, -46, -48, 60, 66, 62, 68, 104, 102, 98, 104, 48, 46, 66, 64, 48, 38, 34, 32, -160, -158, -150, -144, -160, -162, -174, -168, -224, -218, -222, -224, -136, -138, -142, -152

Offset

1,2

Comments

This is a fractal sequence (see scatterplot for 2^k<=n<=2^(k+1) and various k).

Links

Alois P. Heinz, Table of n, a(n) for n = 1..16384

Maple

b:= proc(n) option remember;
      `if`(n=1, 1, add(b(k)*(-1)^floor(n/k), k=1..n-1))
    end:
a:= proc(n) option remember; b(n) +`if`(n=1, 0, a(n-1)) end:
seq(a(n), n=1..100);  # Alois P. Heinz, Sep 12 2011

Mathematica

b[1] = 1;
b[n_] := b[n] = Sum[b[k] (-1)^Floor[n/k], {k, 1, n-1}];
Array[b, 100] // Accumulate (* Jean-François Alcover, Nov 12 2020 *)

Crossrefs

Cf. A194577.

Sequence in context: A240697 A271230 A112824 * A308022 A001100 A218831

Adjacent sequences: A195130 A195131 A195132 * A195134 A195135 A195136

Keyword

sign,look

Author

Benoit Cloitre, Sep 09 2011

Status

approved