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A122994
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a(n) = a(n-1)+9*a(n-2) initialized with a(0)=1, a(1)=3.
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4
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1, 3, 12, 39, 147, 498, 1821, 6303, 22692, 79419, 283647, 998418, 3551241, 12537003, 44498172, 157331199, 557814747, 1973795538, 6994128261, 24758288103, 87705442452, 310530035379, 1099879017447, 3894649335858, 13793560492881, 48845404515603, 172987448951532
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| The two roots of the denominator of the g.f. (for Binet's formula) are -0.393486... and 0.2823756...
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (1,9).
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FORMULA
| G.f.: -(1+2*x)/(-1+x+9*x^2). a(n)= A015445(n)+2*A015445(n-1). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 12 2009]
a(n) = (1/2+5*sqrt(37)/74) *(1/2+sqrt(37)/2)^(n-1) +(1/2-5*sqrt(37)/74) *(1/2-sqrt(37)/2)^(n-1). [From Antonio Alberto Olivares, Jun 07 2011]
a(n) = Sum_{k, 0<=k<=n} A103631(n,k)*3^k. - DELEHAM Philippe, Dec 17 2011
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MATHEMATICA
| CoefficientList[Series[(-2 z - 1)/(9 z^2 + z - 1), {z, 0, 200}], z] (* From Vladimir Joseph Stephan Orlovsky, Jun 11 2011 *)
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CROSSREFS
| Cf. A026597.
Sequence in context: A123109 A110153 A183366 * A062311 A034956 A032093
Adjacent sequences: A122991 A122992 A122993 * A122995 A122996 A122997
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KEYWORD
| nonn,easy
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AUTHOR
| Roger Bagula (rlbagulatftn(AT)yahoo.com), Sep 22 2006
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EXTENSIONS
| Definition replaced with the Deleham recurrence of Mar 2009 by the Assoc. Editors of the OEIS, Mar 12 2010
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