|
%I #25 Sep 08 2022 08:45:18
%S 0,2,11,56,285,1452,7406,37816,193295,989002,5065051,25963276,
%T 133199780,683904902,3514119571,18069536436,92975574865,478701242652,
%U 2466137174466,12711910214796,65558648361175,338267429484502
%N Expansion of g.f.: x*(2 - 9*x - 4*x^2)/((1 - 5*x + x^2)*(1 - 5*x - x^2)).
%H G. C. Greubel, <a href="/A106804/b106804.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 (10,-25,0,1).
%F G.f.: x*(2 - 9*x - 4*x^2)/((1 - 5*x + x^2)*(1 - 5*x - x^2)).
%F a(n) = (1/2)*((A052918(n) - 2*A052918(n-1)) - (A004254(n+1) - 6*A004254(n))). - _G. C. Greubel_, Sep 11 2021
%t M = {{0,0,0,1}, {1,5,0,0}, {0,1,0,0}, {0,0,1,5}}; v[1]= {0,1,1,2}; v[n_]:= v[n]= M.v[n-1]; Table[v[n][[1]], {n, 20}]
%t LinearRecurrence[{10,-25,0,1},{0,2,11,56},30] (* _Harvey P. Dale_, Nov 29 2018 *)
%o (Magma) I:=[0,2,11,56]; [n le 4 select I[n] else 10*Self(n-1) - 25*Self(n-2) + Self(n-4): n in [1..31]]; // _G. C. Greubel_, Sep 11 2021
%o (Sage)
%o def A106804_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P( x*(2-9*x-4*x^2)/((1-5*x+x^2)*(1-5*x-x^2)) ).list()
%o A106804_list(30) # _G. C. Greubel_, Sep 11 2021
%Y Cf. A004254, A052918.
%K nonn,easy
%O 0,2
%A _Roger L. Bagula_, May 30 2005
%E Edited by the Associate Editors of the OEIS, Apr 09 2009
%E Mathematica code fixed by _Olivier Gérard_, Dec 13 2011
|
