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A153191 a(n) = 9*a(n-1) + 6*a(n-2); a(0)=0, a(1)=1. 2
0, 1, 9, 87, 837, 8055, 77517, 745983, 7178949, 69086439, 664851645, 6398183439, 61572760821, 592543948023, 5702332097133, 54876252562335, 528100265643813, 5082159906168327, 48908040749377821, 470665326181410351 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (9, 6).

FORMULA

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

a(n) = ((9 + sqrt(105))^n - (9 - sqrt(105))^n)/(2^n * sqrt(105)), with n >= 0. - Paolo P. Lava, Dec 22 2008

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

Table[Simplify[((9+Sqrt[105])^n -(9-Sqrt[105])^n)/(2^n*Sqrt[105])], {n, 0, 25}] (* Vladimir Joseph Stephan Orlovsky, Jan 27 2011, modified by G. C. Greubel, Jun 01 2019 *)

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

PROG

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

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

(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

CROSSREFS

Cf. A015579, A099371.

Sequence in context: A055725 A219123 A144852 * A223277 A267265 A152264

Adjacent sequences:  A153188 A153189 A153190 * A153192 A153193 A153194

KEYWORD

nonn

AUTHOR

Zerinvary Lajos, Dec 20 2008

EXTENSIONS

Formula corrected by Philippe Deléham, Dec 20 2008

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

STATUS

approved

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Last modified January 17 20:36 EST 2020. Contains 330987 sequences. (Running on oeis4.)