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A084059
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a(n)=4a(n-1)+2a(n-2), a(0)=1,a(1)=2.
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6
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1, 2, 10, 44, 196, 872, 3880, 17264, 76816, 341792, 1520800, 6766784, 30108736, 133968512, 596091520, 2652303104, 11801395456, 52510188032, 233643543040, 1039594548224, 4625665278976, 20581850212352, 91578731407360
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Binomial transform of A002533.
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (4,2).
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FORMULA
| E.g.f.: exp(2x)cosh(sqrt(6)x).
a(n)=((2+sqrt(6))^n+(2-sqrt(6))^n)/2. - Paul Barry (pbarry(AT)wit.ie), May 13 2003
a(n)=sum{k=0..floor(n/2), C(n,2k)*2^(n-k)*3^k}; - Paul Barry (pbarry(AT)wit.ie), Jan 15 2007
G.f.:(1-2x)/(1-4x-2x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 07 2009]
a(n) = A090017(n+1)-2*A090017(n). - R. J. Mathar, Apr 05 2011
a(n) = Sum_{k, 0<=k<=n} A201730(n,k)*5^k . - DELEHAM Philippe, Dec 06 2011
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PROG
| (Other) sage: [lucas_number2(n, 4, -2)/2 for n in xrange(0, 23)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 14 2009]
(MAGMA) [n le 2 select n else 4*Self(n-1)+ 2*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Apr 05 2011
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CROSSREFS
| Cf. A090017.
Sequence in context: A068551 A099919 A100397 * A084609 A105485 A151313
Adjacent sequences: A084056 A084057 A084058 * A084060 A084061 A084062
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), May 10 2003
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