A153191 a(n) = 9*a(n-1) + 6*a(n-2); a(0)=0, a(1)=1.

0, 1, 9, 87, 837, 8055, 77517, 745983, 7178949, 69086439, 664851645, 6398183439, 61572760821, 592543948023, 5702332097133, 54876252562335, 528100265643813, 5082159906168327, 48908040749377821, 470665326181410351

Offset: 0

Author

Zerinvary Lajos, Dec 20 2008

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (9, 6).

Crossrefs

Cf. A015579, A099371.

Programs

Magma

I:=[0,1]; [n le 2 select I[n] else 9*Self(n-1) + 6*Self(n-2): n in [1..25]]; // G. C. Greubel, Jan 24 2018

Maple

a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=9*a[n-1]+6*a[n-2]od: seq(a[n], n=0..33);

Mathematica

LinearRecurrence[{9,6}, {0,1}, 25] (* G. C. Greubel, Jan 24 2018 *)

PARI

x='x+O('x^25); concat([0], Vec(x/(1-9*x-6*x^2))) \\ G. C. Greubel, Jan 24 2018

Sage

[lucas_number1(n,9,-6) for n in range(0, 25)]#  Zerinvary Lajos, Apr 26 2009

Formula

G.f.: x/(1 - 9*x - 6*x^2).

Extensions

Formula corrected by Philippe Deléham, Dec 20 2008

Edited by N. J. A. Sloane, Dec 21 2008