|
%I #10 Oct 19 2022 08:06:21
%S 4,6,8,12,20,34,56,88,132,190,264,356,468,602,760,944,1156,1398,1672,
%T 1980,2324,2706,3128,3592,4100,4654,5256,5908,6612,7370,8184,9056,
%U 9988,10982,12040,13164,14356
%N Generator for the finite sequence A053016.
%H G. C. Greubel, <a href="/A136254/b136254.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F a(n) = n^3/3 - n^2 + 8n/3 + 4.
%F G.f.: (8*x^2 - 10*x + 4)/(x^4 - 4*x^3 + 6*x^2 - 4*x + 1). - _Alexander R. Povolotsky_, Mar 31 2008
%F From _G. C. Greubel_, Feb 23 2017: (Start)
%F E.g.f.: (1/3)*(12 + 6*x + x^3)*exp(x).
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End)
%t CoefficientList[Series[(8*x^2 - 10*x + 4)/(x^4 - 4*x^3 + 6*x^2 - 4*x + 1), {x, 0, 50}], x] (* _G. C. Greubel_, Feb 23 2017 *)
%t LinearRecurrence[{4,-6,4,-1},{4,6,8,12},40] (* _Harvey P. Dale_, Jul 23 2018 *)
%o (PARI) x='x+O('x^50); Vec((8*x^2 - 10*x + 4)/(x^4 - 4*x^3 + 6*x^2 - 4*x + 1)) \\ _G. C. Greubel_, Feb 23 2017
%Y Cf. A053016.
%K nonn,easy
%O 0,1
%A _Rolf Pleisch_, Mar 17 2008
|
