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A080424 a(n) = 3*a(n-1) + 18*a(n-2), a(0)=0, a(1)=1. 7
0, 1, 3, 27, 135, 891, 5103, 31347, 185895, 1121931, 6711903, 40330467, 241805655, 1451365371, 8706597903, 52244370387, 313451873415, 1880754287211, 11284396583103, 67706766919107, 406239439253175, 2437440122303451 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The ratio a(n+1)/a(n) converges to 6 as n approaches infinity. - Felix P. Muga II, Mar 10 2014

LINKS

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).

FORMULA

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

MATHEMATICA

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 *)

PROG

(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

CROSSREFS

Cf. A079773, A051958, A015441.

Sequence in context: A063263 A204809 A034200 * A285008 A001796 A174613

Adjacent sequences:  A080421 A080422 A080423 * A080425 A080426 A080427

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Feb 24 2003

STATUS

approved

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Last modified December 15 22:36 EST 2018. Contains 318155 sequences. (Running on oeis4.)