|
%I #26 Sep 08 2022 08:44:41
%S 1,18,229,2538,26197,259290,2498293,23637546,220808533,2043771642,
%T 18789409717,171872944074,1566234297109,14231753285274,
%U 129035291862901,1167964212866922,10558204018573525,95349518886691386
%N Expansion of 1/((1-2x)*(1-7x)*(1-9x)).
%H Vincenzo Librandi, <a href="/A016312/b016312.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 (18,-95,126).
%F a(n) = ((9^n - 2^n)/7 - (7^n - 2^n)/5)/2, n >= 2. - _Zerinvary Lajos_, Jun 05 2009
%F a(n) = 18*a(n-1) - 95*a(n-2) + 126*a(n-3). - _Vincenzo Librandi_, Jun 26 2013
%t CoefficientList[Series[1 / ((1 - 2 x) (1 - 7 x) (1 - 9 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jun 26 2013 *)
%o (Sage) [((9^n - 2^n)/7-(7^n - 2^n)/5)/2 for n in range(2,20)] # _Zerinvary Lajos_, Jun 05 2009
%o (Magma) I:=[1,18,229]; [n le 3 select I[n] else 18*Self(n-1)-95*Self(n-2)+126*Self(n-3): n in [1..20]]; /* or */ m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-2*x)*(1-7*x)*(1-9*x)))); // _Vincenzo Librandi_, Jun 26 2013
%o (PARI) x='x+O('x^99); Vec(1/((1-2*x)*(1-7*x)*(1-9*x))) \\ _Altug Alkan_, Sep 21 2018
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
|
