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%I #17 Sep 08 2022 08:44:45
%S 1,22,337,4522,57253,705334,8574889,103567234,1246828045,14986093486,
%T 179978152081,2160608272186,25932522746677,311221616234278,
%U 3734847461630713,44819297962008178,537838346143305949
%N Expansion of 1/((1-x)(1-3x)(1-6x)(1-12x)).
%H Vincenzo Librandi, <a href="/A021534/b021534.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 (22,-147,342,-216).
%F a(0)=1, a(1)=22; for n>1, a(n) = 18*a(n-1) -72*a(n-2) +(3^n - 1)/2. - _Vincenzo Librandi_, Jul 10 2013
%F a(0)=1, a(1)=22, a(2)=337, a(3)=4522; for n>3, a(n) = 22*a(n-1) -147*a(n-2) +342*a(n-3) -216*a(n-4). - _Vincenzo Librandi_, Jul 11 2013
%F a(n) = -1/110-(12/5)*6^n+(1/2)*3^n+(32/11)*12^n - _Robert Israel_, Apr 06 2014
%t CoefficientList[Series[1 / ((1 - x) (1 - 3 x) (1 - 6 x) (1 - 12 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 11 2013 *)
%t LinearRecurrence[{22,-147,342,-216},{1,22,337,4522},20] (* _Harvey P. Dale_, Mar 05 2019 *)
%o (Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-3*x)*(1-6*x)*(1-12*x)))); /* or */ I:=[1, 22, 337, 4522]; [n le 4 select I[n] else 22*Self(n-1)-147*Self(n-2)+342*Self(n-3)-216*Self(n-4): n in [1..25]]; // _Vincenzo Librandi_, Jul 11 2013
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.