A017161 - OEIS

%I #34 Mar 11 2025 03:18:13

%S 1,19,265,3355,41041,495859,5964505,71633035,859838881,10319056099,

%T 123832690345,1486008529915,17832167873521,213986278134739,

%U 2567836397009785,30814041016037995,369768509243184961,4437222179250275779,53246666424718954825,638959998192652301275

%N Expansion of g.f. 1/((1 - 3*x)*(1 - 4*x)*(1 - 12*x)).

%H Vincenzo Librandi, <a href="/A017161/b017161.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 (19,-96,144).

%F a(n) = 3^n - 2*4^n + 2*12^n. - _R. J. Mathar_, Jun 23 2013

%F From _Vincenzo Librandi_, Jun 26 2013: (Start)

%F a(n) = 19*a(n-1) - 96*a(n-2) + 144*a(n-3).

%F a(n) = 16*a(n-1) - 48*a(n-2) + 3^n. (End)

%t CoefficientList[Series[1 / ((1 - 3 x) (1 - 4 x) (1 - 12 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jun 26 2013 *)

%o (Magma) I:=[1,19,265]; [n le 3 select I[n] else 19*Self(n-1)-96*Self(n-2)+144*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)*(1-12*x)))); // _Vincenzo Librandi_, Jun 26 2013

%o (PARI) my(x='x+O('x^20)); Vec(1/((1-3*x)*(1-4*x)*(1-12*x))) \\ _Altug Alkan_, Sep 23 2018

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_