%I #17 Sep 08 2022 08:44:44
%S 1,21,303,3745,42711,464961,4918663,51086385,524227671,5336085601,
%T 54018566823,544793838225,5480212349431,55028108373441,
%U 551863246323783,5529708675105265,55374624529091991,554289026917064481
%N Expansion of 1/((1-4*x)*(1-7*x)*(1-10*x)).
%H Vincenzo Librandi, <a href="/A019618/b019618.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (21,-138,280).
%F a(n) = (2*4^(n+1) -7^(n+2) +5*10^(n+1))/9. - _R. J. Mathar_, Nov 11 2012
%F a(0)=1, a(1)=21, a(2)=303; for n>2, a(n) = 21*a(n-1) -138*a(n-2) +280*a(n-3). - _Vincenzo Librandi_, Jul 03 2013
%F a(n) = 17*a(n-1) -70*a(n-2) +4^n. - _Vincenzo Librandi_, Jul 03 2013
%t CoefficientList[Series[1 / ((1 - 4 x) (1 - 7 x) (1 - 10 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 03 2013 *)
%t LinearRecurrence[{21,-138,280},{1,21,303},30] (* _Harvey P. Dale_, Mar 09 2017 *)
%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-4*x)*(1-7*x)*(1-10*x)))); /* or */ I:=[1, 21, 303]; [n le 3 select I[n] else 21*Self(n-1)-138*Self(n-2)+280*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Jul 03 2013
%o (PARI) x='x+O('x^30); Vec(1/((1-4*x)*(1-7*x)*(1-10*x))) \\ _G. C. Greubel_, Aug 24 2018
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_