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A135247 a(n) = 3*a(n-1) + 2*a(n-2) - 6*a(n-3). 1
0, 0, 1, 3, 11, 33, 103, 309, 935, 2805, 8431, 25293, 75911, 227733, 683263, 2049789, 6149495, 18448485, 55345711, 166037133, 498111911, 1494335733, 4483008223, 13449024669, 40347076055, 121041228165, 363123688591, 1089371065773, 3268113205511, 9804339616533 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,2,-6).

FORMULA

a(n) = -14*(-sqrt(2))^n*(-56-84*sqrt(2))^(-1) + 22*2^(1/2*n)*(-56-84*sqrt(2))^(-1) + 12*2^(1/2*n)*sqrt(2)*(-56-84*sqrt(2))^(-1) - 12*3^n*sqrt(2)*(-56-84*sqrt(2))^(-1) - 8*3^n*(-56-84*sqrt(2))^(-1), with n>=0 - Paolo P. Lava, Jun 09 2008

G.f.: x^2/(1 - 3*x - 2*x^2 + 6*x^3). - G. C. Greubel, Oct 04 2016

MAPLE

seq(coeff(series(x^2/(1-3*x-2*x^2+6*x^3), x, n+1), x, n), n = 0..30); # G. C. Greubel, Nov 20 2019

MATHEMATICA

LinearRecurrence[{3, 2, -6}, {0, 0, 1}, 30] (* Harvey P. Dale, Jun 27 2015 *)

PROG

(PARI) my(x='x+O('x^30)); concat([0, 0], Vec(x^2/(1-3*x-2*x^2+6*x^3))) \\ G. C. Greubel, Nov 20 2019

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 30); [0, 0] cat Coefficients(R!( x^2/(1-3*x-2*x^2+6*x^3) )); // G. C. Greubel, Nov 20 2019

(Sage)

def A135247_list(prec):

    P.<x> = PowerSeriesRing(ZZ, prec)

    return P( x^2/(1-3*x-2*x^2+6*x^3) ).list()

A135247_list(30) # G. C. Greubel, Nov 20 2019

(GAP) a:=[0, 0, 1];; for n in [4..30] do a[n]:=3*a[n-1]+2*a[n-2]-6*a[n-3]; od; a; # G. C. Greubel, Nov 20 2019

CROSSREFS

Sequence in context: A124640 A081673 A081250 * A094539 A295092 A032199

Adjacent sequences:  A135244 A135245 A135246 * A135248 A135249 A135250

KEYWORD

nonn

AUTHOR

Paul Curtz, Feb 15 2008

EXTENSIONS

More terms from Harvey P. Dale, Jun 27 2015

STATUS

approved

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Last modified January 18 11:29 EST 2022. Contains 350454 sequences. (Running on oeis4.)