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Search: id:A163064
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| A163064 |
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a(n) = ((3+sqrt(5))*(4+sqrt(5))^n+(3-sqrt(5))*(4-sqrt(5))^n)/2. |
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+0
3
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| 3, 17, 103, 637, 3963, 24697, 153983, 960197, 5987763, 37339937, 232854103, 1452093517, 9055353003, 56469795337, 352149479663, 2196028088597, 13694580432483, 85400334485297, 532562291125063, 3321094649662237
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OFFSET
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0,1
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COMMENT
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Binomial transform of A098648 without initial 1. Fourth binomial transform of A163114. Inverse binomial transform of A163065.
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FORMULA
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a(n) = 8*a(n-1)-11*a(n-2) for n > 1; a(0) = 3, a(1) = 17.
G.f.: (3-7*x)/(1-8*x+11*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)*(4+r)^n+(3-r)*(4-r)^n)/2: n in [0..19] ]; [ 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. A098648, A163114, A163065.
Sequence in context: A074565 A054365 A116886 this_sequence A020069 A020024 A036551
Adjacent sequences: A163061 A163062 A163063 this_sequence A163065 A163066 A163067
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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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