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Search: id:A048654
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| A048654 |
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a(n)=2a(n-1)+a(n-2); a(0)=1, a(1)=4. |
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+0
20
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| 1, 4, 9, 22, 53, 128, 309, 746, 1801, 4348, 10497, 25342, 61181, 147704, 356589, 860882, 2078353, 5017588, 12113529, 29244646, 70602821, 170450288, 411503397, 993457082, 2398417561, 5790292204
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Generalized Pellian with second term equal to 4.
The generalized Pellian with second term equal to s has the terms a(n) = A000129(n)*s+A00129(n-1). The generating function is -(1+s*x-2*x)/(-1+2*x+x^2) . - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 22 2007
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REFERENCES
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A. F. Horadam, Pell Identities, Fibonacci Quarterly, Vol. 9, No. 3, 1971, pp. 245-252.
A. F. Horadam, Basic Properties of a Certain Generalized Sequence of Numbers, Fibonacci Quarterly, Vol. 3, No. 3, 1965, pp. 161-176.
A. F. Horadam, Special Properties of the Sequence W(a, b; p, q), Fibonacci Quarterly, Vol. 5, No. 5, 1967, pp. 424-434.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..300
Tanya Khovanova, Recursive Sequences
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FORMULA
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a(n)=[ (3+sqrt(2))(1+sqrt(2))^n - (3-sqrt(2))(1-sqrt(2))^n ]/2*sqrt(2).
A048654(n) = 2P(n+2) - 3P(n+1), P(n) = Pell numbers (A000129) - Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Oct 27 2004
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MAPLE
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with(combinat): a:=n->2*fibonacci(n-1, 2)+fibonacci(n, 2): seq(a(n), n=1..26); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 04 2008
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CROSSREFS
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Cf. A001333, A000129, A048655, A038761, A100525.
Sequence in context: A032288 A076859 A042833 this_sequence A122626 A135025 A070713
Adjacent sequences: A048651 A048652 A048653 this_sequence A048655 A048656 A048657
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KEYWORD
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easy,nice,nonn
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AUTHOR
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Barry E. Williams
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