|
%I #18 Sep 08 2022 08:44:43
%S 1,17,199,1997,18487,163205,1398223,11743469,97300423,798539093,
%T 6509186047,52798905341,426744275959,3440074001381,27677315556271,
%U 222358880070413,1784513217331495,14309958928401269,114682790953126495
%N Expansion of 1/((1-3x)(1-6x)(1-8x)).
%H Vincenzo Librandi, <a href="/A017932/b017932.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 (17,-90,144).
%F a(0)=1, a(1)=17, a(2)=199; for n>2, a(n) = 17*a(n-1) -90*a(n-2) +144*a(n-3). - _Vincenzo Librandi_, Jul 02 2013
%F a(n) = 14*a(n-1) -48*a(n-2) +3^n. - _Vincenzo Librandi_, Jul 02 2013
%F a(n) =(3*8^(n+2) - 5*6^(n+2) + 2*3^(n+2))/30. [_Yahia Kahloune_, Jul 06 2013]
%p a:= n-> (Matrix(3, (i, j)-> `if`(i=j-1, 1, `if`(j=1, [17, -90, 144][i], 0)))^n)[1, 1]: seq(a(n), n=0..25); # _Alois P. Heinz_, Jul 02 2013
%t CoefficientList[Series[1 / ((1 - 3 x) (1 - 6 x) (1 - 8 x)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Jul 02 2013 *)
%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-3*x)*(1-6*x)*(1-8*x)))); /* or */ I:=[1, 17, 199]; [n le 3 select I[n] else 17*Self(n-1)-90*Self(n-2)+144*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Jul 02 2013
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.
|
