A016239 - OEIS

%I #22 Sep 22 2025 16:00:24

%S 1,18,247,3120,38221,462558,5570227,66940380,803772841,9647715498,

%T 115784793007,1389478551240,16674047790661,200090099366838,

%U 2401088821796587,28813104008531700,345757438837243681

%N Expansion of 1/((1-x)*(1-5*x)*(1-12*x)).

%H G. C. Greubel, <a href="/A016239/b016239.txt">Table of n, a(n) for n = 0..900</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (18,-77,60).

%F a(0)=1, a(1)=18; for n>1, a(n)=17*a(n-1)-60*a(n-2)+1. - _Vincenzo Librandi_, Feb 10 2011

%F a(n) = (4*12^(n+2) - 11*5^(n+2) + 7)/308. - _Yahia Kahloune_, Aug 13 2013

%F E.g.f.: (1/308)*(7*exp(x) - 275*exp(5*x) + 576*exp(12*x)). - _G. C. Greubel_, Jan 30 2022

%t LinearRecurrence[{18,-77,60}, {1,18,247}, 40] (* _G. C. Greubel_, Jan 30 2022 *)

%t CoefficientList[Series[1/((1-x)(1-5x)(1-12x)),{x,0,20}],x] (* _Harvey P. Dale_, Jun 18 2025 *)

%o (PARI) a(n) = (4*12^(n+2) - 11*5^(n+2) + 7)/308; \\ _Joerg Arndt_, Aug 13 2013

%o (Magma) [(4*12^(n+2) -11*5^(n+2) +7)/308: n in [0..40]]; // _G. C. Greubel_, Jan 30 2022

%o (SageMath) [(4*12^(n+2) -11*5^(n+2) +7)/308 for n in (0..40)] # _G. C. Greubel_, Jan 30 2022

%Y Cf. A003463, A016238.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_