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%I #19 Dec 05 2024 13:52:12
%S 1,24,403,5886,80113,1046748,13329631,166873722,2064748525,
%T 25337358072,309091680859,3754490630358,45462401712937,
%U 549225447909396,6623795021132887,79783347069641394,960080426180248549
%N Expansion of 1/((1-x)(1-2x)(1-9x)(1-12x)).
%H Vincenzo Librandi, <a href="/A021304/b021304.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (24,-173,366,-216).
%F a(n) = (28*12^(n+3) - 55*9^(n+3) + 132*2^(n+3) - 105)/9240. - _Yahia Kahloune_, Jul 07 2013
%F a(0)=1, a(1)=24, a(2)=403, a(3)=5886; for n>3, a(n) = 24*a(n-1) -173*a(n-2) +366*a(n-3) -216*a(n-4). - _Vincenzo Librandi_, Jul 09 2013
%F a(0)=1, a(1)=24; for n>1, a(n) = 21*a(n-1) -108*a(n-2) +2^n -1. - _Vincenzo Librandi_, Jul 09 2013
%t CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 9 x) (1 -12 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 09 2013 *)
%o (Magma) I:=[1, 24, 403, 5886]; [n le 4 select I[n] else 24*Self(n-1)-173*Self(n-2)+366*Self(n-3)-216*Self(n-4): n in [1..25]]; // _Vincenzo Librandi_, Jul 09 2013
%o (Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-9*x)*(1-12*x)))); // _Vincenzo Librandi_, Jul 09 2013
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_