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Search: id:A163611
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| A163611 |
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a(n) = ((5+2*sqrt(2))*(5+sqrt(2))^n+(5-2*sqrt(2))*(5-sqrt(2))^n)/2. |
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+0
3
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| 5, 29, 175, 1083, 6805, 43141, 274895, 1756707, 11244485, 72040589, 461782735, 2960893803, 18987935125, 121778793781, 781065429935, 5009742042387, 32132915535365, 206105088378749, 1321993826474095, 8479521232029723
(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 A163610. Fifth binomial transform of A163888.
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FORMULA
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a(n) = 10*a(n-1)-23*a(n-2) for n > 1; a(0) = 5, a(1) = 29.
G.f.: (5-21*x)/(1-10*x+23*x^2).
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PROGRAM
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(MAGMA) Z<x>:= PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((5+2*r)*(5+r)^n+(5-2*r)*(5-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Aug 06 2009]
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CROSSREFS
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Cf. A163610, A163888.
Sequence in context: A088349 A137625 A083066 this_sequence A160906 A163073 A139174
Adjacent sequences: A163608 A163609 A163610 this_sequence A163612 A163613 A163614
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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 01 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), Aug 06 2009
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