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A017998 Expansion of 1/((1-3x)(1-7x)(1-9x)). 1
1, 19, 250, 2830, 29611, 295729, 2866900, 27241660, 255258421, 2367929839, 21805655950, 199711092490, 1821621686431, 16564149750349, 150264234543400, 1360686332771320, 12304334591153641, 111146114623005259 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (19,-111,189).

FORMULA

a(0)=1, a(1)=19, a(2)=250, a(n)=19*a(n-1)-111*a(n-2)+189*a(n-3). - Harvey P. Dale, Oct 31 2011

a(n) = (2*9^(n+2) - 3*7^(n+2) + 3^(n+2))/24. - Yahia Kahloune, Jun 30 2013

a(n) = 16*a(n-1) -63*a(n-2) +3^n. - Vincenzo Librandi, Jul 02 2013

MAPLE

a:= n-> (Matrix(3, (i, j)-> `if`(i=j-1, 1, `if`(j=1, [19, -111, 189][i], 0)))^n)[1, 1]: seq(a(n), n=0..25);  # Alois P. Heinz, Jul 02 2013

MATHEMATICA

CoefficientList[Series[1/((1-3x)(1-7x)(1-9x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{19, -111, 189}, {1, 19, 250}, 30] (* Harvey P. Dale, Oct 31 2011 *)

PROG

(MAGMA) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-3*x)*(1-7*x)*(1-9*x)))); /* or */ I:=[1, 19, 250]; [n le 3 select I[n] else 19*Self(n-1)-111*Self(n-2)+189*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 02 2013

CROSSREFS

Sequence in context: A019443 A021229 A021464 * A018912 A021202 A125454

Adjacent sequences:  A017995 A017996 A017997 * A017999 A018000 A018001

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified July 27 08:33 EDT 2021. Contains 346304 sequences. (Running on oeis4.)