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A019041 Expansion of 1/((1-4x)(1-5x)(1-12x)). 2
1, 21, 313, 4125, 51601, 630741, 7630633, 91892685, 1104403201, 13261555461, 159183299353, 1910426955645, 22926277062001, 275121159824181, 3301483361726473, 39617948633641005, 475416129363276001 (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 (21,-128,240).

FORMULA

a(n) = 2*4^n -25*5^n/7 +18*12^n/7. - R. J. Mathar, Jun 29 2013

a(0)=1, a(1)=21, a(2)=313; for n>2, a(n)= 21*a(n-1) -128*a(n-2) +240*a(n-3). - Vincenzo Librandi, Jul 02 2013

a(n) = 17*a(n-1) -60*a(n-2) +4^n. - Vincenzo Librandi, Jul 02 2013

MATHEMATICA

CoefficientList[Series[1 / ((1 - 4 x) (1 - 5 x) (1 - 12 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 02 2013 *)

PROG

(MAGMA) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-4*x)*(1-5*x)*(1-12*x)))); /* or */ I:=[1, 21, 313]; [n le 3 select I[n] else 21*Self(n-1)-128*Self(n-2)+240*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 02 2013

CROSSREFS

Sequence in context: A157088 A226990 A016321 * A021214 A016318 A017954

Adjacent sequences:  A019038 A019039 A019040 * A019042 A019043 A019044

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified May 22 00:25 EDT 2019. Contains 323472 sequences. (Running on oeis4.)