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Search: id:A164588
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| A164588 |
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((3 + sqrt(18))*(5 + sqrt(8))^n + (3 - sqrt(18))*(5 - sqrt(8))^n)/6 . |
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+0
2
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| 1, 9, 73, 577, 4529, 35481, 277817, 2174993, 17027041, 133295529, 1043495593, 8168931937, 63949894289, 500627099961, 3919122796697, 30680567267633, 240180585132481, 1880236207775049, 14719292130498313, 115228905772807297, 902061091509601649
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Binomial transform of A057084. Second binomial transform of A002315. Third binomial transform of A108051 without initial 0. Fourth binomial transform of A096980. Fifth binomial transform of A094015.
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FORMULA
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a(n) = 10*a(n-1)-17*a(n-2) for n > 1; a(0) = 1, a(1) = 9.
G.f.: (1-x)/(1-10*x+17*x^2).
a(n)=10*a(n-1)-17*a(n-2), with a(0)=1, a(1)=9. [From Paolo P. Lava (ppl(AT)spl.at), Aug 25 2009]
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PROGRAM
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(MAGMA) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((3+3*r)*(5+2*r)^n+(3-3*r)*(5-2*r)^n)/6: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Aug 24 2009]
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CROSSREFS
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Cf. A057084, A002315, A108051, A096980, A094015.
Sequence in context: A079927 A126641 A081627 this_sequence A023001 A015454 A121246
Adjacent sequences: A164585 A164586 A164587 this_sequence A164589 A164590 A164591
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KEYWORD
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nonn
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AUTHOR
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Al Hakanson (hawkuu(AT)gmail.com), Aug 17 2009
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EXTENSIONS
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Extended by Klaus Brockhaus and R. J. Mathar Aug 24 2009
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