%I #16 Sep 08 2022 08:44:44
%S 4,9,20,44,96,209,455,990,2154,4686,10194,22175,48236,104922,228220,
%T 496402,1079712,2348431,5107921,11109837,24164007,52556739,114310581,
%U 248624146,540753403,1176127722,2558050589,5563694894
%N a(n) = 3*a(n-1) - 4*a(n-3) + a(n-6).
%D R. K. Guy, personal communication.
%H G. C. Greubel, <a href="/A019493/b019493.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (3,0,-4,0,0,1).
%F G.f.: (4 - 3*x - 7*x^2 + x^5)/(1 - 3*x + 4*x^3 - x^6). - _R. J. Mathar_, Feb 11 2016
%t LinearRecurrence[{3,0,-4,0,0,1}, {4,9,20,44,96,209}, 30] (* _G. C. Greubel_, Mar 24 2019 *)
%o (PARI) my(x='x+O('x^30)); Vec((4-3*x-7*x^2+x^5 )/(1-3*x+4*x^3-x^6)) \\ _G. C. Greubel_, Mar 24 2019
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (4-3*x-7*x^2+x^5 )/(1-3*x+4*x^3-x^6) )); // _G. C. Greubel_, Mar 24 2019
%o (Sage) ((4-3*x-7*x^2+x^5 )/(1-3*x+4*x^3-x^6)).series(x, 30).coefficients(x, sparse=False) # _G. C. Greubel_, Mar 24 2019
%Y Matches A019492 up to n <= 10.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_
|