A190980 a(n) = 9*a(n-1) - 3*a(n-2), with a(0)=0, a(1)=1.

0, 1, 9, 78, 675, 5841, 50544, 437373, 3784725, 32750406, 283399479, 2452344093, 21220898400, 183631053321, 1589016784689, 13750257902238, 118985270766075, 1029616663187961, 8909594156393424, 77097497417976933, 667148694292612125, 5773045756379578326

Offset: 0

Author

Vladimir Joseph Stephan Orlovsky, May 24 2011

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..500
• Index entries for linear recurrences with constant coefficients, signature (9,-3).

Crossrefs

Cf. A190958 (index to generalized Fibonacci sequences).

Programs

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

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 *)

PARI

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

Formula

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