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A135522
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a(n) = 2*a(n-1) + 3*a(n-2).
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15
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2, 3, 12, 33, 102, 303, 912, 2733, 8202, 24603, 73812, 221433, 664302, 1992903, 5978712, 17936133, 53808402, 161425203, 484275612, 1452826833, 4358480502, 13075441503, 39226324512, 117678973533, 353036920602, 1059110761803
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Also: inverse binomial transform of A135520. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 17 2008
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index to sequences with linear recurrences with constant coefficients, signature (2,3).
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FORMULA
| O.g.f.: (5/(1-3*x)+3/(1+x))/4. a(n) = (5*3^n+3*(-1)^n)/4. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 23 2008
G.f.: (x-2)/(3*x^2+2*x-1) [From Harvey P. Dale, Mar 14 2011]
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MATHEMATICA
| f[n_]:=3/(n+2); x=2; Table[x=f[x]; Numerator[x], {n, 0, 5!}] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Mar 11 2010]
Transpose[NestList[Join[Rest[#], ListCorrelate[{3, 2}, #]]&, {2, 3}, 30]][[1]] (* From Harvey P. Dale, Mar 14 2011 *)
CoefficientList[Series[(x-2)/(3x^2+2x-1), {x, 0, 30}], x] (* From Harvey P. Dale, Mar 14 2011 *)
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PROG
| (PARI) a(n)=(5*3^n+3*(-1)^n)/4 \\ Charles R Greathouse IV, Jun 01 2011
(MAGMA) [(5*3^n+3*(-1)^n)/4: n in [0..40]]; // Vincenzo Librandi, Jun 02 2011
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CROSSREFS
| Cf. A060925.
Sequence in context: A076424 A165301 A072440 * A107240 A099171 A012307
Adjacent sequences: A135519 A135520 A135521 * A135523 A135524 A135525
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KEYWORD
| nonn,easy
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AUTHOR
| Paul Curtz (bpcrtz(AT)free.fr), Feb 19 2008
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 23 2008
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