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Search: id:A163062
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| A163062 |
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a(n) = ((3+sqrt(5))*(1+sqrt(5))^n+(3-sqrt(5))*(1-sqrt(5))^n)/2. |
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+0
3
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| 3, 8, 28, 88, 288, 928, 3008, 9728, 31488, 101888, 329728, 1067008, 3452928, 11173888, 36159488, 117014528, 378667008, 1225392128, 3965452288, 12832473088, 41526755328, 134383403008, 434873827328, 1407281266688
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OFFSET
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0,1
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COMMENT
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Binomial transform of A163114. Inverse binomial transform of A163063.
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FORMULA
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a(n) = 2*a(n-1)+4*a(n-2) for n > 1; a(0) = 3, a(1) = 8.
G.f.: (3+2*x)/(1-2*x-4*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)*(1+r)^n+(3-r)*(1-r)^n)/2: n in [0..23] ]; [ 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. A163114, A163063.
Sequence in context: A005641 A148845 A148846 this_sequence A148847 A148848 A148849
Adjacent sequences: A163059 A163060 A163061 this_sequence A163063 A163064 A163065
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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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