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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
OFFSET
0,2
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
KEYWORD
nonn,easy
STATUS
approved