|
|
A092119
|
|
EULER transform of A001511.
|
|
6
|
|
|
1, 1, 3, 4, 10, 13, 26, 35, 66, 88, 150, 202, 331, 442, 688, 919, 1394, 1848, 2716, 3590, 5174, 6796, 9589, 12542, 17440, 22680, 31055, 40208, 54420, 70096, 93772, 120256, 159380, 203436, 267142, 339573, 442478, 560050, 724302, 913198, 1173375, 1473622
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
Given A000041, P(x) = A(x)/A(x^2) with P(x) = (1 + x + 2x^2 + 3x^3 + 5x^4 + 7x^5 + ...),
A(x) = (1 + x + 3x^2 + 4x^3 + 10x^4 + 13x^5 + ...),
A(x^2) = (1 + x^2 + 3x^4 + 4x^6 + 10x^8 + ...), where A092119 = (1, 1, 3, 4, 10, ...) = Euler transform of the ruler sequence, A001511. (End)
Let M = triangle A173238 as an infinite lower triangular matrix. Then A092119 = lim_{n->infinity} M^n. Let P(x) = polcoeff A000041 = (1 + x + 2x^2 + 3x^3 + ...), and A(x) = polcoeff A092119. Then P(x) = A(x) / A(x^2), an example of a conjectured infinite set of operations (cf. A173238). - Gary W. Adamson, Feb 13 2010
|
|
LINKS
|
|
|
FORMULA
|
G.f.: 1/Product_{k>=0} P(x^(2^k)) where P(x) = Product_{k>=1} (1 - x^k). - Joerg Arndt, Jun 21 2011
|
|
MAPLE
|
# Uses EulerTransform from A358369.
t := EulerTransform(n -> padic[ordp](2*n, 2)):
|
|
MATHEMATICA
|
m = 42;
|
|
PROG
|
(PARI) N=66; x='x+O('x^N); /* that many terms */
gf=1/prod(e=0, ceil(log(N)/log(2)), eta(x^(2^e)));
Vec(gf) /* show terms */ /* Joerg Arndt, Jun 21 2011 */
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|