%I #23 Nov 19 2024 00:52:34
%S 1,28,533,8648,128889,1824276,24950461,333078016,4367420897,
%T 56484732044,722650676709,9164986526904,115404823162825,
%U 1444532800672132,17990818115880077,223110488408176112
%N Expansion of 1/((1-x)*(1-4*x)*(1-11*x)*(1-12*x)).
%H Vincenzo Librandi, <a href="/A022000/b022000.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 (28,-251,752,-528).
%F a(n) = (105*12^(n+3) - 132*11^(n+3) + 55*4^(n+3) - 28)/9240. [_Yahia Kahloune_, Jun 28 2013]
%F a(0)=1, a(1)=28, a(2)=533, a(3)=8648; for n>3, a(n) = 28*a(n-1) -251*a(n-2) +752*a(n-3) -528*a(n-4). - _Vincenzo Librandi_, Jul 12 2013
%t CoefficientList[Series[1 / ((1 - x) (1 - 4 x) (1 - 11 x) (1 - 12 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 12 2013 *)
%o (Magma) I:=[1,28,533,8648]; [n le 4 select I[n] else 28*Self(n-1)-251*Self(n-2)+752*Self(n-3)-528*Self(n-4): n in [1..25]]; // _Vincenzo Librandi_, Jul 12 2013
%o (Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-4*x)*(1-11*x)*(1-12*x)))); // _Vincenzo Librandi_, Jul 12 2013
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_