%I #14 Sep 08 2022 08:44:45
%S 1,23,357,4675,55781,628803,6831637,72401555,754291461,7764923683,
%T 79263766517,804302170035,8126850016741,81868359076163,
%U 822960967286997,8260021493532115,82815918789863621,829686041539878243
%N Expansion of 1/((1-6x)(1-7x)(1-10x)).
%H Vincenzo Librandi, <a href="/A020572/b020572.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 (23,-172,420).
%F a(n) = 9*6^n -49*7^n/3 +25*10^n/3. - _R. J. Mathar_, Jun 30 2013
%F a(0)=1, a(1)=23, a(2)=357; for n>2, a(n) = 23*a(n-1) -172*a(n-2) +420*a(n-3). - _Vincenzo Librandi_, Jul 04 2013
%F a(n) = 17*a(n-1) -70*a(n-2) +6^n. - _Vincenzo Librandi_, Jul 04 2013
%t CoefficientList[Series[1 / ((1 - 6 x) (1 - 7 x) (1 - 10 x)), {x, 0, 20}],x] (* _Vincenzo Librandi_, Jul 04 2013 *)
%t LinearRecurrence[{23,-172,420},{1,23,357},20] (* _Harvey P. Dale_, Sep 24 2016 *)
%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-6*x)*(1-7*x)*(1-10*x)))); /* or */ I:=[1, 23, 357]; [n le 3 select I[n] else 23*Self(n-1)-172*Self(n-2)+420*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Jul 04 2013
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.
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