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A181353 a(n) = 9*a(n-1) + 3*a(n-2); a(0)=0, a(1)=1. 3
0, 1, 9, 84, 783, 7299, 68040, 634257, 5912433, 55114668, 513769311, 4789267803, 44644718160, 416170266849, 3879466556121, 36163709805636, 337111787919087, 3142497220688691, 29293810349955480, 273071784811665393, 2545527494354854977 (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, 3).

FORMULA

a(n) = ((9+sqrt(93))^n - (9-sqrt(93))^n)/(2^n*sqrt(93)). - Rolf Pleisch, May 14 2011

G.f.: x/(1-9*x-3*x^2). - Philippe Deléham, Nov 21 2011

a(n+1) = Sum_{k=0..n} A099097(n,k)*3^k. - Philippe Deléham, Nov 21 2011

MATHEMATICA

Join[{a=0, b=1}, Table[c=9*b+3*a; a=b; b=c, {n, 60}]]

LinearRecurrence[{9, 3}, {0, 1}, 30] (* G. C. Greubel, Jan 24 2018 *)

PROG

(PARI) x='x+O('x^30); concat([0], Vec(x/(1-9*x-3*x^2))) \\ G. C. Greubel, Jan 24 2018

(MAGMA) I:=[0, 1]; [n le 2 select I[n] else 9*Self(n-1) + 3*Self(n-2): n in [1..30]];

CROSSREFS

Cf. A015579, A099371.

Sequence in context: A272582 A037595 A037686 * A152056 A086627 A024118

Adjacent sequences:  A181350 A181351 A181352 * A181354 A181355 A181356

KEYWORD

nonn,easy

AUTHOR

Vladimir Joseph Stephan Orlovsky, Jan 27 2011

STATUS

approved

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Last modified March 19 04:23 EDT 2019. Contains 321311 sequences. (Running on oeis4.)