A020594 - OEIS

%I #20 Sep 08 2022 08:44:45

%S 1,26,460,6920,95536,1254176,15958720,199053440,2450711296,

%T 29915173376,363095649280,4390419138560,52953377222656,

%U 637600367845376,7668561507696640,92162065025761280,1107062216886255616

%N Expansion of 1/((1-6x)(1-8x)(1-12x)).

%H Vincenzo Librandi, <a href="/A020594/b020594.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 (26,-216,576).

%F a(n) = (2*12^(n+2) - 6*8^(n+2) + 4*6^(n+2))/48. [_Yahia Kahloune_, Jun 30 2013]

%F a(0)=1, a(1)=26, a(2)=460; for n>2, a(n) = 26*a(n-1) -216*a(n-2) +576*a(n-3). - _Vincenzo Librandi_, Jul 04 2013

%F a(n) = 20*a(n-1) -96*a(n-2) +6^n. - _Vincenzo Librandi_, Jul 04 2013

%t CoefficientList[Series[1 / ((1 - 6 x) (1 - 8 x) (1 - 12 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 04 2013 *)

%t LinearRecurrence[{26,-216,576},{1,26,460},20] (* _Harvey P. Dale_, Nov 10 2021 *)

%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-6*x)*(1-8*x)*(1-12*x)))); /* or */ I:=[1, 26, 460]; [n le 3 select I[n] else 26*Self(n-1)-216*Self(n-2)+576*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Jul 04 2013

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.