A018206 - OEIS

%I #16 Sep 08 2022 08:44:44

%S 1,24,403,5850,78601,1007364,12509263,151886670,1813607701,

%T 21378247704,249446413723,2886767617890,33183014997601,

%U 379298878576044,4315144805143783,48895164279003510,552132521336304301

%N Expansion of 1/((1-3x)(1-10x)(1-11x)).

%H Vincenzo Librandi, <a href="/A018206/b018206.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 (24,-173,330).

%F a(0)=1, a(1)=24, a(2)=403; for n>2, a(n) = 24*a(n-1) -173*a(n-2) +330*a(n-3). - _Vincenzo Librandi_, Jul 02 2013

%F a(n) = 21*a(n-1) -110*a(n-2) +3^n. - _Vincenzo Librandi_, Jul 02 2013

%F a(n) = (7*11^(n+2) - 8*10^(n+2) + 3^(n+2))/56. [_Yahia Kahloune_, Jul 06 2013]

%t CoefficientList[Series[1 / ((1 - 3 x) (1 - 10 x) (1 - 11 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 02 2013 *)

%t LinearRecurrence[{24,-173,330},{1,24,403},20] (* _Harvey P. Dale_, Nov 25 2013 *)

%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-3*x)*(1-10*x)*(1-11*x)))); /* or */ I:=[1, 24, 403]; [n le 3 select I[n] else 24*Self(n-1)-173*Self(n-2)+330*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Jul 02 2013

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.