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A080424
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a(n) = 3*a(n-1) + 18*a(n-2), a(0)=0, a(1)=1.
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7
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0, 1, 3, 27, 135, 891, 5103, 31347, 185895, 1121931, 6711903, 40330467, 241805655, 1451365371, 8706597903, 52244370387, 313451873415, 1880754287211, 11284396583103, 67706766919107, 406239439253175, 2437440122303451
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OFFSET
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0,3
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COMMENTS
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The ratio a(n+1)/a(n) converges to 6 as n approaches infinity. - Felix P. Muga II, Mar 10 2014
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
F. P. Muga II, Extending the Golden Ratio and the Binet-de Moivre Formula, March 2014; Preprint on ResearchGate.
Index entries for linear recurrences with constant coefficients, signature (3,18).
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FORMULA
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G.f.: x/((1+3*x)*(1-6*x)).
a(n) = (6^n - (-3)^n)/9.
a(n+1) = 6*a(n) + (-3)^n. - Paul Curtz, Jun 07 2011
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MATHEMATICA
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Join[{a=0, b=1}, Table[c=3*b+18*a; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Feb 01 2011 *)
f[n_] := (6^n - (-3)^n)/9; Array[f, 22, 0] (* Robert G. Wilson v, Aug 13 2011 *)
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PROG
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(PARI) a(n)=(6^n-(-3)^n)/9 \\ Charles R Greathouse IV, Jun 10 2011
(MAGMA)[(6^n-(-3)^n)/9: n in [0..30]]; // Vincenzo Librandi, Aug 13 2011
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CROSSREFS
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Cf. A079773, A051958, A015441.
Sequence in context: A204809 A034200 A306442 * A285008 A001796 A174613
Adjacent sequences: A080421 A080422 A080423 * A080425 A080426 A080427
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry, Feb 24 2003
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STATUS
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approved
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