|
%I #14 Sep 08 2022 08:44:45
%S 1,25,427,6229,83779,1076341,13459699,165601573,2017494787,
%T 24431946517,294797887891,3549239159557,42674698231075,
%U 512696237681653,6156632228705203,73909998565124581,887135686636037443
%N Expansion of 1/((1-6x)(1-7x)(1-12x)).
%H Vincenzo Librandi, <a href="/A020577/b020577.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 (25,-198,504).
%F a(n) = 6*6^n -49*7^n/5 +24*12^n/5. - _R. J. Mathar_, Jun 30 2013
%F a(0)=1, a(1)=25, a(2)=427; for n>2, a(n) = 25*a(n-1) -198*a(n-2) +504*a(n-3). - _Vincenzo Librandi_, Jul 04 2013
%F a(n) = 19*a(n-1) -84*a(n-2) +6^n. - _Vincenzo Librandi_, Jul 04 2013
%t CoefficientList[Series[1 / ((1 - 6 x) (1 - 7 x) (1 - 12 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 04 2013 *)
%t LinearRecurrence[{25,-198,504},{1,25,427},30] (* _Harvey P. Dale_, Sep 27 2014 *)
%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-6*x)*(1-7*x)*(1-12*x)))); /* or */ I:=[1, 25, 427]; [n le 3 select I[n] else 25*Self(n-1)-198*Self(n-2)+504*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Jul 04 2013
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.
|
