|
%I #29 Jan 31 2022 03:18:12
%S 1,14,141,1246,10277,81270,624877,4710062,34985973,256995046,
%T 1871524733,13536029598,97364345989,697223254742,4974599780109,
%U 35386420442254,251090274984725,1777943916226758,12567479361589405,88703587219138430,625312500662044581
%N Expansion of 1/((1-x)*(1-6*x)*(1-7*x)).
%H G. C. Greubel, <a href="/A016241/b016241.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (14,-55,42).
%F a(0)=1, a(1)=14, a(n) = 13*a(n-1) - 42*a(n-2) + 1. - _Vincenzo Librandi_, Feb 10 2011
%F a(n) = (1 - 6^(n+2) + 5*7^(n+1))/30. - _Vladimir Joseph Stephan Orlovsky_, Jul 21 2011
%F a(0)=1, a(1)=14, a(2)=141, a(n) = 14*a(n-1) - 55*a(n-2) + 42*a(n-3). - _Harvey P. Dale_, Aug 05 2011
%F E.g.f.: (1/30)*(exp(x) - 36*exp(6*x) + 35*exp(7*x)). - _G. C. Greubel_, Jan 30 2022
%t Table[(1 -6^(n+2) +5*7^(n+1))/30, {n, 40}] (* or *) CoefficientList[Series[1/((1-z)(1-6*z)(1-7*z)), {z, 0, 40}], z] (* _Vladimir Joseph Stephan Orlovsky_, Jul 21 2011 *)
%t LinearRecurrence[{14,-55,42},{1,14,141},40] (* _Harvey P. Dale_, Aug 05 2011 *)
%o (PARI) Vec(1/((1-x)*(1-6*x)*(1-7*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012
%o (Magma) [(1 -6^(n+2) +5*7^(n+1))/30 : n in [0..40]]; // _G. C. Greubel_, Jan 30 2022
%o (Sage) [(1 -6^(n+2) +5*7^(n+1))/30 for n in (0..40)] # _G. C. Greubel_, Jan 30 2022
%Y Cf. A016218, A016228, A016249.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
|
