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Search: id:A145301
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| A145301 |
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a(n) = ((6+sqrt(6))^n+(6-sqrt(6))^n)/2. |
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+0
5
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| 1, 6, 42, 324, 2628, 21816, 182952, 1540944, 13002768, 109804896, 927575712, 7836761664, 66213868608, 559463573376, 4727146822272, 39941854665984, 337487851323648, 2851598575904256, 24094547371141632, 203586611176571904
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Binomial transform is A152262, inverse binomial transform is A146962.
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FORMULA
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a(n)=12*a(n-1)-30*a(n-2). G.f.: (1-6x)/(1-12x+30x^2). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 10 2008]
a(n)=Sum_{k, 0<=k<=n}6^k*A098158(n,k). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 14 2008]
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PROGRAM
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(MAGMA) Z<x>:= PolynomialRing(Integers()); N<r6>:=NumberField(x^2-6); S:=[ ((6+r6)^n+(6-r6)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 20 2008]
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CROSSREFS
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Cf. A098158, A152262, A146962.
Sequence in context: A162968 A034171 A153293 this_sequence A107266 A142985 A118351
Adjacent sequences: A145298 A145299 A145300 this_sequence A145302 A145303 A145304
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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), Oct 06 2008
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 10 2008
Corrected definition. - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 15 2008
Edited by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jul 08 2009
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