%I #21 Jan 27 2025 14:39:52

%S 1,21,308,3942,47271,547407,6213586,69694464,776054741,8602512633,

%T 95089014384,1049208790266,11563904125411,127361197423299,

%U 1402080935995502,15430644646390548,169791371563507281,1868085050371321005,20551595296294241740,226086166454705682510,2487078158370047768351

%N Expansion of 1/((1-x)*(1-2*x)*(1-7*x)*(1-11*x)).

%H Vincenzo Librandi, <a href="/A021244/b021244.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (21,-133,267,-154).

%F a(n)=(11^(n+3) - 3*7^(n+3) + 8*2^(n+3) - 6)/360. [_Yahia Kahloune_, Jun 30 2013]

%F a(0)=1, a(1)=21, a(2)=308, a(3)=3942; for n>3, a(n) = 21*a(n-1) -133*a(n-2) +267*a(n-3) -154*a(n-4). - _Vincenzo Librandi_, Jul 08 2013

%F a(0)=1, a(1)=21; for n>1, a(n) = 18*a(n-1) -77*a(n-2) +2^n -1. - _Vincenzo Librandi_, Jul 08 2013

%t CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 7 x) (1 - 11 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 08 2013 *)

%t LinearRecurrence[{21,-133,267,-154},{1,21,308,3942},20] (* _Harvey P. Dale_, May 31 2020 *)

%o (Magma) I:=[1, 21, 308, 3942]; [n le 4 select I[n] else 21*Self(n-1)-133*Self(n-2)+267*Self(n-3)-154*Self(n-4): n in [1..25]]; // _Vincenzo Librandi_, Jul 08 2013

%o (Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-7*x)*(1-11*x)))); // _Vincenzo Librandi_, Jul 08 2013

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_