A218021 Shifts 4 places left under Euler transform with a(0)=0 and a(n)=1 for n < 4.

0, 1, 1, 1, 1, 1, 2, 3, 5, 7, 12, 18, 30, 47, 78, 125, 209, 341, 571, 946, 1592, 2663, 4503, 7594, 12898, 21891, 37334, 63691, 109039, 186816, 320913, 551829, 950842, 1640149, 2833866, 4901658, 8490019, 14720477, 25553525, 44401638, 77232183, 134457819

Offset

0,7

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

N. J. A. Sloane, Transforms

Formula

a(n) ~ c * d^n / n^(3/2), where d = 1.8065918193702780027972... and c = 1.041173202249532389463... . - Vaclav Kotesovec, Jun 23 2014

G.f.: x + x^2 + x^3 + x^4 / Product_{n>=1} (1 - x^n)^a(n). - Ilya Gutkovskiy, May 08 2019

Maple

with(numtheory):
b:= proc(n) option remember; `if`(n=0, 1,
      (add(add(d*a(d), d= divisors(j)) *b(n-j), j=1..n))/n)
    end:
a:= n-> `if`(n<4, signum(n), b(n-4)):
seq(a(n), n=0..45);

Mathematica

b[n_] := b[n] = If[n == 0, 1, (Sum[Sum[d*a[d], {d, Divisors[j]}]*b[n - j], {j, 1, n }])/n]; a[n_] := If[n < 4, Sign[n], b[n - 4]]; Table[a[n], {n, 0, 41}] (* Jean-François Alcover, Aug 01 2013, after Alois P. Heinz *)

Crossrefs

Column k=4 of A144018.

Cf. A316076.

Sequence in context: A013983 A257863 A169986 * A137713 A326490 A191385

Adjacent sequences: A218018 A218019 A218020 * A218022 A218023 A218024

Keyword

nonn,eigen

Author

Alois P. Heinz, Oct 18 2012

Status

approved