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Search: id:A084120
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| A084120 |
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a(n)=6a(n-1)-3a(n-2), a(0)=1,a(1)=3. |
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+0
6
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| 1, 3, 15, 81, 441, 2403, 13095, 71361, 388881, 2119203, 11548575, 62933841, 342957321, 1868942403, 10184782455, 55501867521, 302456857761, 1648235544003, 8982042690735, 48947549512401, 266739169002201
(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 of A084059.
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FORMULA
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a(n)=((3+sqrt(6))^n+(3-sqrt(6))^n)/2; G.f.: (1-3x)/(1-6x+3x^2); E.g.f. : exp(3x)cosh(sqrt(6)x).
a(n)=3^n*sum{k=0..floor(n/2), C(n, 2k)(2/3)^k}; - Paul Barry (pbarry(AT)wit.ie), Sep 10 2005
a(n)/a(n-1) tends to (3 + sqrt(6)) = 5.445489742... - Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 19 2008
a(n)=Sum_{k, 0<=k<=n}A147720(n,k)*3^k. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 15 2008]
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PROGRAM
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(PARI) a(n)=if(n<0, 0, polsym(x^2-6*x+3, n)[1+n]/2)
sage: [lucas_number2(n, 6, 3)/2 for n in xrange(0, 27)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 08 2008
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CROSSREFS
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Cf. A138395.
Sequence in context: A020044 A024338 A003448 this_sequence A163470 A122868 A015680
Adjacent sequences: A084117 A084118 A084119 this_sequence A084121 A084122 A084123
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), May 13 2003
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