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Search: id:A163063
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| A163063 |
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a(n ) = ((3+sqrt(5))*(2+sqrt(5))^n+(3-sqrt(5))*(2-sqrt(5))^n)/2. |
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+0
3
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| 3, 11, 47, 199, 843, 3571, 15127, 64079, 271443, 1149851, 4870847, 20633239, 87403803, 370248451, 1568397607, 6643838879, 28143753123, 119218851371, 505019158607, 2139295485799, 9062201101803, 38388099893011
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Binomial transform of A163062. Second binomial transform of A163114. Inverse binomial transform of A098648 without initial 1.
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FORMULA
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a(n) = 4*a(n-1)+a(n-2) for n > 1; a(0) = 3, a(1) = 11.
G.f.: (3-x)/(1-4*x-x^2).
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PROGRAM
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(MAGMA) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-5); S:=[ ((3+r)*(2+r)^n+(3-r)*(2-r)^n)/2: n in [0..21] ]; [ Integers()!S[j]: j in [1..#S] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jul 21 2009]
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CROSSREFS
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Cf. A163062, A163114, A098648.
Sequence in context: A030814 A030976 A112567 this_sequence A151142 A151143 A151144
Adjacent sequences: A163060 A163061 A163062 this_sequence A163064 A163065 A163066
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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), Jul 20 2009
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EXTENSIONS
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Edited and extended beyond a(5) by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jul 21 2009
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