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A218021 Shifts 4 places left under Euler transform with a(0)=0 and a(n)=1 for n < 4. 3

%I

%S 0,1,1,1,1,1,2,3,5,7,12,18,30,47,78,125,209,341,571,946,1592,2663,

%T 4503,7594,12898,21891,37334,63691,109039,186816,320913,551829,950842,

%U 1640149,2833866,4901658,8490019,14720477,25553525,44401638,77232183,134457819

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

%H Alois P. Heinz, <a href="/A218021/b218021.txt">Table of n, a(n) for n = 0..1000</a>

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%F a(n) ~ c * d^n / n^(3/2), where d = 1.8065918193702780027972... and c = 1.041173202249532389463... . - _Vaclav Kotesovec_, Jun 23 2014

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

%p with(numtheory):

%p b:= proc(n) option remember; `if`(n=0, 1,

%p (add(add(d*a(d), d= divisors(j)) *b(n-j), j=1..n))/n)

%p end:

%p a:= n-> `if`(n<4, signum(n), b(n-4)):

%p seq(a(n), n=0..45);

%t 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-Fran├žois Alcover_, Aug 01 2013, after _Alois P. Heinz_ *)

%Y Column k=4 of A144018.

%Y Cf. A316076.

%K nonn,eigen

%O 0,7

%A _Alois P. Heinz_, Oct 18 2012

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Last modified May 24 20:53 EDT 2019. Contains 323534 sequences. (Running on oeis4.)