|
%I #30 Sep 08 2022 08:44:41
%S 1,15,157,1431,12229,101199,823789,6649287,53436757,428483583,
%T 3431885821,27471332343,219836173285,1758953038767,14072683703053,
%U 112585721544999,900702823089013,7205690916768351,57645801049792285
%N Expansion of 1/((1-3x)(1-4x)(1-8x)).
%H Vincenzo Librandi, <a href="/A016849/b016849.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 (15,-68,96).
%F a(n) = 15*a(n-1) - 68*a(n-2) + 96*a(n-3); a(0)=1, a(1)=15, a(2)=157. - _Harvey P. Dale_, Mar 23 2012
%F a(n) = 9*3^n/5 - 4*4^n + 16*8^n/5. - _R. J. Mathar_, Jun 23 2013
%F a(n) = 12*a(n-1) - 32*a(n-2) + 3^n. - _Vincenzo Librandi_, Jun 26 2013
%t CoefficientList[Series[1/((1-3x)(1-4x)(1-8x)),{x,0,30}],x] (* or *) LinearRecurrence[{15,-68,96},{1,15,157},30] (* _Harvey P. Dale_, Mar 23 2012 *)
%o (Magma) I:=[1, 15, 157]; [n le 3 select I[n] else 15*Self(n-1)-68*Self(n-2) +96*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Jun 26 2013
%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-3*x)*(1-4*x)*(1-8*x)))); // _Vincenzo Librandi_, Jun 26 2013
%o (PARI) x='x+O('x^20); Vec(1/((1-3*x)*(1-4*x)*(1-8*x))) \\ _Altug Alkan_, Sep 23 2018
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
|
