A015579 Expansion of g.f. x/(1 - 9*x - 2*x^2).

0, 1, 9, 83, 765, 7051, 64989, 599003, 5521005, 50887051, 469025469, 4323003323, 39845080845, 367251734251, 3384955769949, 31199105398043, 287561860122285, 2650454951896651, 24429218287314429, 225163874489623163, 2075333306981237325, 19128327511810382251

Offset: 0

Author

Olivier Gérard

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (9,2).

Crossrefs

Cf. A099371.

Programs

Magma

[n le 2 select n-1 else 9*Self(n-1) + 2*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 14 2012

Mathematica

Join[{a=0,b=1},Table[c=9*b+2*a;a=b;b=c,{n,60}]] (* Vladimir Joseph Stephan Orlovsky, Jan 27 2011 *)
LinearRecurrence[{9, 2}, {0, 1}, 30] (* Vincenzo Librandi, Nov 14 2012 *)
CoefficientList[Series[x/(1-9x-2x^2),{x,0,30}],x] (* Harvey P. Dale, Aug 14 2023 *)

PARI

x='x+O('x^30); concat([0], Vec(x/(1-9*x-2*x^2))) \\ G. C. Greubel, Jan 06 2018

Sage

[lucas_number1(n,9,-2) for n in range(0, 19)] # Zerinvary Lajos, Apr 26 2009

Formula

a(n) = 9*a(n-1) + 2*a(n-2).

E.g.f.: 2*exp(9*x/2)*sinh(sqrt(89)*x/2)/sqrt(89). - Stefano Spezia, Apr 06 2023

Extensions

Extended by T. D. Noe, May 23 2011