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A122120 a(n) = 4*a(n-1) + 9*a(n-2), for n>1, with a(0)=1, a(1)=3. 1
1, 3, 21, 111, 633, 3531, 19821, 111063, 622641, 3490131, 19564293, 109668351, 614752041, 3446023323, 19316861661, 108281656551, 606978381153, 3402448433571, 19072599164661, 106912432560783, 599303122725081 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (4,9).

FORMULA

a(n) = Sum_{k=0..n} 3^(n-k)*A055380(n,k).

G.f.: (1-x)/(1-4*x-9*x^2).

lim_n -> infinity} a(n+1)/a(n) -> 2 + sqrt(13).

a(n) = -(1/26)*sqrt(13)*(2-sqrt(13))^n + (1/2)*(2+sqrt(13))^n+(1/26)*(2+sqrt(13))^n*sqrt(13) + (1/2)*(2-sqrt(13))^n, with n>=0. -  Paolo P. Lava, Nov 19 2008

MATHEMATICA

CoefficientList[Series[(1-x)/(1-4*x-9*x^2), {x, 0, 30}], x] (* G. C. Greubel, Feb 26 2019 *)

PROG

(PARI) my(x='x+O('x^30)); Vec((1-x)/(1-4*x-9*x^2)) \\ G. C. Greubel, Feb 26 2019

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1-x)/(1-4*x-9*x^2) )); // G. C. Greubel, Feb 26 2019

(Sage) ((1-x)/(1-4*x-9*x^2)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Feb 26 2019

CROSSREFS

First differences of A015533.

Binomial transform of A091914.

Sequence in context: A054147 A233582 A043012 * A080952 A183404 A309670

Adjacent sequences:  A122117 A122118 A122119 * A122121 A122122 A122123

KEYWORD

nonn,easy

AUTHOR

Philippe Deléham, Oct 19 2006

STATUS

approved

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Last modified August 13 04:54 EDT 2020. Contains 336442 sequences. (Running on oeis4.)