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%I #34 Dec 18 2023 00:31:08
%S 1,9,9,19,37,65,121,223,409,753,1385,2547,4685,8617,15849,29151,53617,
%T 98617,181385,333619,613621,1128625,2075865,3818111,7022601,12916577,
%U 23757289,43696467,80370333,147824089,271890889,500085311,919800289,1691776489
%N a(n) = a(n-1) + a(n-2) + a(n-3), with a(0) = 1, a(1) = a(2) = 9.
%C Part of a group of sequences defined by a(0), a(1)=a(2), a(n)=a(n-1)+a(n-2)+a(n-3) which is a subgroup of sequences with linear recurrences and constant coefficients listed in the index. See comments in A214727.
%H Robert Price, <a href="/A214831/b214831.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 (1,1,1).
%F G.f.: (1+8*x-x^2)/(1-x-x^2-x^3).
%F a(n) = -A000073(n) + 8*A000073(n+1) + A000073(n+2). - _G. C. Greubel_, Apr 24 2019
%t LinearRecurrence[{1,1,1},{1,9,9},40] (* _Harvey P. Dale_, Oct 11 2017 *)
%o (PARI) Vec((x^2-8*x-1)/(x^3+x^2+x-1) + O(x^40)) \\ _Michel Marcus_, Jul 08 2014
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+8*x-x^2)/(1-x-x^2-x^3) )); // _G. C. Greubel_, Apr 24 2019
%o (SageMath) ((1+8*x-x^2)/(1-x-x^2-x^3)).series(x, 40).coefficients(x, sparse=False) # _G. C. Greubel_, Apr 24 2019
%o (GAP) a:=[1,9,9];; for n in [4..40] do a[n]:=a[n-1]+a[n-2]+a[n-3]; od; a; # _G. C. Greubel_, Apr 24 2019
%Y Cf. A000213, A000288, A000322, A000383, A060455, A136175, A141036, A141523, A214825-A214831, A244930, A244931.
%K nonn,easy
%O 0,2
%A _Abel Amene_, Aug 07 2012
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