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A145301
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a(n) = 12*a(n-1) - 30*a(n-2) with a(0)=1 and a(1)=6.
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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; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Binomial transform is A152262, inverse binomial transform is A146962.
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FORMULA
| G.f.: (1-6x)/(1-12x+30x^2). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 10 2008]
a(n) = ((6+sqrt(6))^n+(6-sqrt(6))^n)/2.
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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PROG
| (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
| Cf. A098158, A152262, A146962.
Sequence in context: A162968 A034171 A153293 * A107266 A142985 A118351
Adjacent sequences: A145298 A145299 A145300 * A145302 A145303 A145304
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KEYWORD
| nonn
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AUTHOR
| Al Hakanson (hawkuu(AT)gmail.com), Oct 06 2008
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EXTENSIONS
| 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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