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Search: id:A162273
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| A162273 |
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a(n) = ((2+sqrt(3))*(3+sqrt(3))^n+(2-sqrt(3))*(3-sqrt(3))^n)/2. |
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+0
2
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| 2, 9, 42, 198, 936, 4428, 20952, 99144, 469152, 2220048, 10505376, 49711968, 235239552, 1113165504, 5267555712, 24926341248, 117952713216, 558158231808, 2641233111552, 12498449278464, 59143297001472, 279869086338048
(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 A001075 without initial term 1, inverse binomial transform of A162274.
The INVERTi transform yields A007051 without A007051(0). - R. J. Mathar, Jul 07 2009
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FORMULA
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a(n) = 6*a(n-1)-6*a(n-2) for n > 1; a(0) = 2, a(1) = 9.
G.f.: (2-3*x)/(1-6*x+6*x^2).
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MAPLE
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seq(simplify(((2+sqrt(3))*(3+sqrt(3))^n+(2-sqrt(3))*(3-sqrt(3))^n)*1/2), n = 0 .. 22); [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 11 2009]
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PROGRAM
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(MAGMA) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-3); S:=[ ((2+r)*(3+r)^n+(2-r)*(3-r)^n)/2: n in [0..21] ]; [ Integers()!S[j]: j in [1..#S] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jul 05 2009]
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CROSSREFS
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Cf. A001075, A162274.
Sequence in context: A152052 A020038 A056845 this_sequence A092239 A132847 A121365
Adjacent sequences: A162270 A162271 A162272 this_sequence A162274 A162275 A162276
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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), Jun 29 2009
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EXTENSIONS
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Edited and extended beyond a(5) by R. J. Mathar and Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jul 05 2009
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