%I #18 Sep 08 2022 08:44:44

%S 1,21,307,3897,46243,529953,5961259,66380889,735097555,8115781905,

%T 89452902331,985061928201,10842178002787,119303005894977,

%U 1312567620466123,14439652232597433,158844629298359539

%N Expansion of 1/((1-4*x)*(1-6*x)*(1-11*x)).

%H Vincenzo Librandi, <a href="/A019488/b019488.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (21,-134,264).

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

%F 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

%F a(n) = 17*a(n-1) -66*a(n-2) +4^n. - _Vincenzo Librandi_, Jul 03 2013

%t CoefficientList[Series[1/((1-4x)(1-6x)(1-11x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 03 2013 *)

%t LinearRecurrence[{21,-134,264},{1,21,307},20] (* _Harvey P. Dale_, Jan 24 2014 *)

%o (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

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

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

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

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_