A173241 Euler transform of A051064, the ruler function sequence for k=3.

1, 1, 2, 4, 6, 9, 16, 22, 33, 51, 71, 100, 147, 199, 275, 384, 515, 692, 944, 1242, 1645, 2186, 2847, 3706, 4848, 6231, 8019, 10330, 13153, 16729, 21305, 26864, 33858, 42658, 53366, 66668, 83277, 103378, 128200, 158846, 195895, 241237, 296860, 363796, 445285, 544465, 663520

Offset

0,3

Comments

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

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

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

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

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Formula

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

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

(1, 1, 2, 1, 1, 2, 1, 1, 3, 1, 1, 2, ...).

Example

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, ...).

Prog

(PARI)  N=66; x='x+O('x^N); /* that many terms */
gf=1/prod(e=0, ceil(log(N)/log(3)), eta(x^(3^e)));
Vec(gf) /* show terms */ /* Joerg Arndt, Jun 21 2011 */

Crossrefs

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

Sequence in context: A372632 A257655 A318026 * A096398 A110538 A288039

Adjacent sequences: A173238 A173239 A173240 * A173242 A173243 A173244

Keyword

nonn

Author

Gary W. Adamson, Feb 13 2010

Extensions

More terms from Joerg Arndt, Jun 21 2011

Status

approved