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A190980 a(n) = 9*a(n-1) - 3*a(n-2), with a(0)=0, a(1)=1. 4
0, 1, 9, 78, 675, 5841, 50544, 437373, 3784725, 32750406, 283399479, 2452344093, 21220898400, 183631053321, 1589016784689, 13750257902238, 118985270766075, 1029616663187961, 8909594156393424, 77097497417976933, 667148694292612125, 5773045756379578326 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (9, -3).

FORMULA

a(n) = (1/69)*sqrt(69)*((9/2+1/2*sqrt(69))^n - (9/2-1/2*sqrt(69))^n). - Paolo P. Lava, May 31 2011

G.f.: x/(1-9*x+3*x^2). - Philippe Deléham, Oct 12 2011

MATHEMATICA

LinearRecurrence[{9, -3}, {0, 1}, 50]

CoefficientList[Series[x/(1-9*x+3*x^2), {x, 0, 50}], x] (* G. C. Greubel, Jan 14 2018 *)

PROG

(PARI) x='x+O('x^30); concat([0], Vec(x/(1-9*x+3*x^2))) \\ G. C. Greubel, Jan 14 2018

(MAGMA) I:=[0, 1]; [n le 2 select I[n] else 9*Self(n-1) - 3*Self(n-2): n in [1..30]]; // G. C. Greubel, Jan 14 2018

CROSSREFS

Cf. A190958 (index to generalized Fibonacci sequences).

Sequence in context: A000445 A046196 A231596 * A254657 A231590 A240797

Adjacent sequences:  A190977 A190978 A190979 * A190981 A190982 A190983

KEYWORD

nonn

AUTHOR

Vladimir Joseph Stephan Orlovsky, May 24 2011

STATUS

approved

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Last modified October 20 01:39 EDT 2018. Contains 316378 sequences. (Running on oeis4.)