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%I #18 Sep 08 2022 08:44:45
%S 1,14,137,1186,9789,79278,637249,5107322,40887077,327183142,
%T 2617726761,20942603058,167543199565,1340352738206,10722843363473,
%U 85782811346794,686262684222453,5490102054386070,43920818177432185,351366550647536930,2810932420866630941
%N Expansion of 1/((1-x)(1-2x)(1-3x)(1-8x)).
%H Vincenzo Librandi, <a href="/A021044/b021044.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 (14,-59,94,-48).
%F a(n) = -(1/14)+(4/3)*2^n-(27/10)*3^n+(256/105)*8^n. - _Antonio Alberto Olivares_, May 12, 2012
%F a(0)=1, a(1)=14; for n>1, a(n) = 11*a(n-1) -24*a(n-2) +2^n - 1. - _Vincenzo Librandi_, Jul 05 2013
%F a(0)=1, a(1)=14, a(2)=137, a(3)=1186; for n>3, a(n) = 14*a(n-1) -59*a(n-2) +94*a(n-3) -48*a(n-4). - _Vincenzo Librandi_, Jul 05 2013
%t CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 3 x) (1 - 8 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 05 2013 *)
%t LinearRecurrence[{14,-59,94,-48},{1,14,137,1186},30] (* _Harvey P. Dale_, Mar 31 2018 *)
%o (Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-3*x)*(1-8*x)))); /* or */ I:=[1, 14, 137, 1186]; [n le 4 select I[n] else 14*Self(n-1)-59*Self(n-2)+94*Self(n-3)-48*Self(n-4): n in [1..25]]; // _Vincenzo Librandi_, Jul 05 2013
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.