A173241 - OEIS

%I #12 Apr 29 2021 08:37:59

%S 1,1,2,4,6,9,16,22,33,51,71,100,147,199,275,384,515,692,944,1242,1645,

%T 2186,2847,3706,4848,6231,8019,10330,13153,16729,21305,26864,33858,

%U 42658,53366,66668,83277,103378,128200,158846,195895,241237,296860,363796,445285,544465,663520

%N Euler transform of A051064, the ruler function sequence for k=3.

%C Let P(x) = polcoeff A000041: (1 + x + 2x^2 + 3x^3 + 5x^4 + 7x^5 + ...) and

%C A(x) = polcoeff A173241: (1 + x + 2x^2 + 4x^3 + 6x^4 + 9x^5 + ...); then

%C P(x) = A(x) / A(x^3).

%C A092119 = Euler transform of the ruler function for k=2: A001511.

%H Seiichi Manyama, <a href="/A173241/b173241.txt">Table of n, a(n) for n = 0..10000</a>

%F G.f.: 1/Product_{k>=0} P(x^(3^k)) where P(x)=Product_{k>=1} (1-x^k). - _Joerg Arndt_, Jun 21 2011

%F Euler transform of A051064, where A051064 = the ruler function for k=3:

%F (1, 1, 2, 1, 1, 2, 1, 1, 3, 1, 1, 2, ...).

%e Equals 1/((1-x)*(1-x^2)*(1-x^3)^2*(1-x^4)*(1-x^5)*(1-x^6)^2*(1-x^7)*...); where in (1-x)^k, k = A051064: (1, 1, 2, 1, 1, 2, 1, 1, 3, ...).

%o (PARI)  N=66; x='x+O('x^N); /* that many terms */

%o gf=1/prod(e=0, ceil(log(N)/log(3)), eta(x^(3^e)));

%o Vec(gf) /* show terms */ /* _Joerg Arndt_, Jun 21 2011 */

%Y Cf. A000041, A001511, A051064, A092119, A173238, A173239.

%K nonn

%O 0,3

%A _Gary W. Adamson_, Feb 13 2010

%E More terms from _Joerg Arndt_, Jun 21 2011