%I #16 Sep 08 2022 08:44:44
%S 1,20,273,3172,33809,342132,3348241,32033924,301669137,2808831124,
%T 25937190929,238042888356,2174659962385,19797924540596,
%U 179763483454737,1628947562960068,14738065844679953,133185374228264148
%N Expansion of 1/((1-4*x)*(1-7*x)*(1-9*x)).
%H Vincenzo Librandi, <a href="/A019613/b019613.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 (20,-127,252).
%F a(n) = 16*4^n/15 -49*7^n/6 +81*9^n/10. - _R. J. Mathar_, Jun 29 2013
%F a(0)=1, a(1)=20, a(2)=273; for n>2, a(n) = 20*a(n-1) -127*a(n-2) +252*a(n-3). - _Vincenzo Librandi_, Jul 03 2013
%F a(n) = 16*a(n-1) -63*a(n-2) +4^n. - _Vincenzo Librandi_, Jul 03 2013
%t CoefficientList[Series[1 / ((1 - 4 x) (1 - 7 x) (1 - 9 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 03 2013 *)
%t LinearRecurrence[{20,-127,252}, {1, 20, 273}, 30] (* _G. C. Greubel_, Aug 24 2018 *)
%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-4*x)*(1-7*x)*(1-9*x)))); /* or */ I:=[1, 20, 273]; [n le 3 select I[n] else 20*Self(n-1)-127*Self(n-2)+252*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)*(1-9*x))) \\ _G. C. Greubel_, Aug 24 2018
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_