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Search: id:A163604
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| A163604 |
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a(n) = ((3+2*sqrt(2))*(4+sqrt(2))^n+(3-2*sqrt(2))*(4-sqrt(2))^n)/2. |
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+0
4
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| 3, 16, 86, 464, 2508, 13568, 73432, 397504, 2151984, 11650816, 63078752, 341518592, 1849046208, 10011109376, 54202228096, 293462293504, 1588867154688, 8602465128448, 46575580861952, 252170135097344, 1365302948711424, 7392041698328576, 40022092304668672
(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 A163606. Inverse binomial transform of A163605.
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FORMULA
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a(n) = 8*a(n-1)-14*a(n-2) for n > 1; a(0) = 3, a(1) = 16.
G.f.: (3-8*x)/(1-8*x+14*x^2).
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PROGRAM
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(MAGMA) Z<x>:= PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((3+2*r)*(4+r)^n+(3-2*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), Aug 07 2009]
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CROSSREFS
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Cf. A163606, A163605.
Sequence in context: A076279 A056369 A056360 this_sequence A151329 A026111 A026330
Adjacent sequences: A163601 A163602 A163603 this_sequence A163605 A163606 A163607
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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) and R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 07 2009
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