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%I #16 Mar 01 2023 14:21:59
%S 1,25,429,6305,85541,1108665,13976989,173186065,2122320981,
%T 25822510505,312717161549,3775431050625,45488017644421,
%U 547320192731545,6579560264282109,79048497300991985,949332313236647861
%N Expansion of 1/((1-5x)(1-8x)(1-12x)).
%H Vincenzo Librandi, <a href="/A020448/b020448.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 (25,-196,480).
%F G.f.: 1/((1-5*x)*(1-8*x)*(1-12*x)).
%F a(n) = 25*5^n/21 -16*8^n/3 +36*12^n/7. - _R. J. Mathar_, Jun 30 2013
%F a(0)=1, a(1)=25, a(2)=429; for n>2, a(n) = 25*a(n-1) -196*a(n-2) +480*a(n-3). - _Vincenzo Librandi_, Jul 03 2013
%F a(n) = 20*a(n-1) -96*a(n-2) +5^n. - _Vincenzo Librandi_, Jul 03 2013
%t CoefficientList[Series[1 / ((1 - 5 x) (1 - 8 x) (1 - 12 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 03 2013 *)
%t LinearRecurrence[{25,-196,480},{1,25,429},20] (* _Harvey P. Dale_, Apr 01 2016 *)
%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-5*x)*(1-8*x)*(1-12*x)))); /* or */ I:=[1, 25, 429]; [n le 3 select I[n] else 25*Self(n-1)-196*Self(n-2)+480*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Jul 03 2013
%K nonn
%O 0,2
%A _N. J. A. Sloane_.
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