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%I #16 Sep 08 2022 08:44:45
%S 1,17,197,1957,17973,157749,1345909,11271029,93191285,763669621,
%T 6218195061,50398593141,407106949237,3280364834933,26383974158453,
%U 211918126207093,1700423007424629,13633852046266485,109253624291872885
%N Expansion of 1/((1-x)(1-2x)(1-6x)(1-8x)).
%H Vincenzo Librandi, <a href="/A021184/b021184.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 (17,-92,172,-96).
%F a(n) = (10*8^(n+3) - 21*6^(n+3) + 35*2^(n+3) - 24)/840. [_Yahia Kahloune_, Jul 05 2013]
%F a(0)=1, a(1)=17; for n>1, a(n) = 14*a(n-1) -48*a(n-2) +2^n -1. - _Vincenzo Librandi_, Jul 07 2013
%F a(0)=1, a(1)=17, a(2)=197, a(3)=1957; for n>3, a(n) = 17*a(n-1) -92*a(n-2) +172*a(n-3) -96*a(n-4). - _Vincenzo Librandi_, Jul 07 2013
%t CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 6 x) (1 - 8 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 07 2013 *)
%t LinearRecurrence[{17,-92,172,-96},{1,17,197,1957},30] (* _Harvey P. Dale_, Jul 17 2015 *)
%o (Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-6*x)*(1-8*x)))); /* or */ I:=[1, 17, 197, 1957]; [n le 4 select I[n] else 17*Self(n-1)-92*Self(n-2)+172*Self(n-3)-96*Self(n-4): n in [1..25]]; // _Vincenzo Librandi_, Jul 07 2013
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.
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