A181353 a(n) = 9*a(n-1) + 3*a(n-2); a(0) = 0, a(1) = 1.

0, 1, 9, 84, 783, 7299, 68040, 634257, 5912433, 55114668, 513769311, 4789267803, 44644718160, 416170266849, 3879466556121, 36163709805636, 337111787919087, 3142497220688691, 29293810349955480, 273071784811665393, 2545527494354854977, 23728962803628690972

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

E.g.f.: 2*exp(9*x/2)*sinh(sqrt(93)*x/2)/sqrt(93). - Stefano Spezia, Apr 06 2023

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 * A370029 A152056 A086627

Adjacent sequences: A181350 A181351 A181352 * A181354 A181355 A181356

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Jan 27 2011

Status

approved