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A019488 Expansion of 1/((1-4*x)*(1-6*x)*(1-11*x)). 1
1, 21, 307, 3897, 46243, 529953, 5961259, 66380889, 735097555, 8115781905, 89452902331, 985061928201, 10842178002787, 119303005894977, 1312567620466123, 14439652232597433, 158844629298359539 (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,-134,264).

FORMULA

a(n) = (10*4^(n+1) - 21*6^(n+1) + 11^(n+2))/35. - R. J. Mathar, Jun 29 2013

a(0)=1, a(1)=21, a(2)=307; for n>2, a(n) = 21*a(n-1) -134*a(n-2) +264*a(n-3). - Vincenzo Librandi, Jul 03 2013

a(n) = 17*a(n-1) -66*a(n-2) +4^n. - Vincenzo Librandi, Jul 03 2013

MATHEMATICA

CoefficientList[Series[1/((1-4x)(1-6x)(1-11x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 03 2013 *)

LinearRecurrence[{21, -134, 264}, {1, 21, 307}, 20] (* Harvey P. Dale, Jan 24 2014 *)

PROG

(MAGMA) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-4*x)*(1-6*x)*(1-11*x))));  /* or */  I:=[1, 21, 307]; [n le 3 select I[n] else 21*Self(n-1)-134*Self(n-2)+264*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 03 2013

(PARI) my(x='x+O('x^20)); Vec(1/((1-4*x)*(1-6*x)*(1-11*x))) \\ G. C. Greubel, Apr 27 2019

(Sage) (1/((1-4*x)*(1-6*x)*(1-11*x))).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 27 2019

(GAP) List([0..20], n-> (10*4^(n+1) - 21*6^(n+1) + 11^(n+2))/35) # G. C. Greubel, Apr 27 2019

CROSSREFS

Sequence in context: A021524 A021268 A018069 * A025929 A021244 A183463

Adjacent sequences:  A019485 A019486 A019487 * A019489 A019490 A019491

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified August 4 15:44 EDT 2020. Contains 336202 sequences. (Running on oeis4.)