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A135064
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Numbers n such that the quintic polynomial x^5-10*n*x^2-24*n has Galois group A_5 over rationals.
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2
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1, 11, 29, 76, 199, 521, 1364, 3571, 9349, 24476, 64079, 167761, 439204, 1149851, 3010349, 7881196, 20633239, 54018521, 141422324, 370248451
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OFFSET
| 1,2
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COMMENTS
| Sequence appears to agree with the Lucas bisection A002878 for n > 1. - Klaus Brockhaus, Nov 18 2007
If this agreement is provable then of course it provides recurrences, generating functions, etc., for this sequence. - N. J. A. Sloane (njas(AT)research.att.com), Nov 24 2007
In A135064 in comparission to A002878 is lack number 4. In this case Galois group of quintic polynomial x^5-40*x^2-96 is Dihedral of order 10. [From Artur Jasinski (grafix(AT)csl.pl), May 27 2010]
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FORMULA
| a(n) for n>0 =(2 - Sqrt[5]) (1/2 (3 - Sqrt[5]))^n + (2 + Sqrt[5]) (1/2 (3 + Sqrt[5]))^n [From Artur Jasinski (grafix(AT)csl.pl), May 27 2010]
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MATHEMATICA
| Table[Expand[(2 - Sqrt[5]) (1/2 (3 - Sqrt[5]))^n + (2 + Sqrt[5]) (1/2 (3 + Sqrt[5]))^n], {n, 1, 20}] (*Artur Jasinski*) [From Artur Jasinski (grafix(AT)csl.pl), May 27 2010]
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CROSSREFS
| Cf. A134538, A134547, A002878.
Sequence in context: A099909 A106881 A106880 * A179502 A053703 A099911
Adjacent sequences: A135061 A135062 A135063 * A135065 A135066 A135067
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KEYWORD
| nonn
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AUTHOR
| Artur Jasinski (grafix(AT)csl.pl), Nov 15 2007
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EXTENSIONS
| a(20) corrected by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Nov 18 2007
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