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Search: id:A046980
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| A046980 |
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Numerators of Taylor series for exp(x)*cos(x). |
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+0
2
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| 1, 1, 0, -1, -1, -1, 0, 1, 1, 1, 0, -1, -1, -1, 0, 1, 1, 1, 0, -1, -1, -1, 0, 1, 1, 1, 0, -1, -1, -1, 0, 1, 1, 1, 0, -1, -1, -1, 0, 1, 1, 1, 0, -1, -1, -1, 0, 1, 1, 1, 0, -1, -1, -1, 0, 1, 1, 1, 0, -1, -1, -1, 0, 1, 1, 1, 0, -1, -1, -1, 0, 1, 1, 1, 0, -1, -1, -1, 0, 1, 1, 1, 0, -1, -1, -1, 0, 1, 1, 1, 0, -1, -1
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Lehmer sequence U_n for R=2 Q=1 [From Artur Jasinski (grafix(AT)csl.pl), Oct 06 2008]
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REFERENCES
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G. W. Caunt, Infinitesimal Calculus, Oxford Univ. Press, 1914, p. 477.
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FORMULA
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G.f.: (1+x-x^3)/(1+x^4).
a(n)=(b^(n+1) - c^(n+1))/(b - c) where b = Sqrt[2]-((1 + I)/Sqrt[2]), c = (1 + I)/Sqrt[2] [From Artur Jasinski (grafix(AT)csl.pl), Oct 06 2008]
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EXAMPLE
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1+1*x-1/3*x^3-1/6*x^4-1/30*x^5+1/630*x^7+1/2520*x^8+1/22680*x^9-...
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MAPLE
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(1+x-x^3)/(1+x^4);
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MATHEMATICA
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b = -((1 + I)/Sqrt[2]) + Sqrt[2]; c = (1 + I)/Sqrt[2]; Table[ Round[(b^n - c^n)/(b - c)], {n, 2, 200}] [From Artur Jasinski (grafix(AT)csl.pl), Oct 06 2008]
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CROSSREFS
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Cf. A046981.
Sequence in context: A014339 A004547 A085369 this_sequence A152822 A118831 A118828
Adjacent sequences: A046977 A046978 A046979 this_sequence A046981 A046982 A046983
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KEYWORD
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sign,frac,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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