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A099867
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a(n) = 5a(n - 1) - a(n - 2), a(0) = 1, a(1) = 9.
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1
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1, 9, 44, 211, 1011, 4844, 23209, 111201, 532796, 2552779, 12231099, 58602716, 280782481, 1345309689, 6445765964, 30883520131, 147971834691, 708975653324, 3396906431929, 16275556506321, 77980876099676, 373628823992059
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| A. F. Horadam, Pell Identities, Fib. Quart., Vol. 9, No. 3, 1971, pps. 245-252.
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LINKS
| Index entries for sequences related to linear recurrences with constant coefficients
Tanya Khovanova, Recursive Sequences
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FORMULA
| |2*a(n) + A099868(n) - A003501(n+1)| = 20*A004254(n)
G.f.: (1+4x)/(1-5x+x^2). a(n) = A004254(n+1)+4*A004254(n). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 11 2008]
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MATHEMATICA
| a[0] = 1; a[1] = 9; a[n_] := a[n] = 5a[n - 1] - a[n - 2]; Table[ a[n], {n, 0, 21}] (from Robert G. Wilson v Dec 14 2004)
LinearRecurrence[{5, -1}, {1, 9}, 30] (* or *) CoefficientList[Series[ (1+4x)/(1-5x+x^2), {x, 0, 30}], x] (* From Harvey P. Dale, June 26 2011 *)
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PROG
| Floretion Algebra Multiplication Program, FAMP
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CROSSREFS
| Cf. A099868, A003501, A004254.
Sequence in context: A084903 A034558 A144109 * A104470 A084016 A125679
Adjacent sequences: A099864 A099865 A099866 * A099868 A099869 A099870
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KEYWORD
| easy,nonn
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AUTHOR
| Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Oct 28 2004
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 14 2004
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