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A092119
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EULER transform of A001511.
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5
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Feb 11 2010: (Start)
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)
Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Feb 13 2010: (Start)
Let M = triangle A173238 as an infinite lower triangular matrix. Then A092119
= Lim_{n->inf} 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). (End)
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LINKS
| N. J. A. Sloane, Transforms
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FORMULA
| G.f.: 1/prod(k>=0, P(x^(2^k)) where P(x)=prod(k>=1, 1-x^k ). [Joerg Arndt, Jun 21 2011]
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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 */
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CROSSREFS
| A000041 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Feb 11 2010]
Cf. A000041, A092119 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Feb 13 2010]
Sequence in context: A092434 A031367 A073443 * A143372 A035594 A167273
Adjacent sequences: A092116 A092117 A092118 * A092120 A092121 A092122
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KEYWORD
| nonn
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 29 2004
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