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%I #34 Sep 08 2022 08:46:02
%S 1,4,4,9,17,30,56,103,189,348,640,1177,2165,3982,7324,13471,24777,
%T 45572,83820,154169,283561,521550,959280,1764391,3245221,5968892,
%U 10978504,20192617,37140013,68311134,125643764,231094911,425049809
%N a(n) = a(n-1) + a(n-2) + a(n-3), with a(0) = 1, a(1) = a(2) = 4.
%C See Comments in A214727.
%H Robert Price, <a href="/A214826/b214826.txt">Table of n, a(n) for n = 0..1000</a>
%H Martin Burtscher, Igor Szczyrba, Rafał Szczyrba, <a href="http://www.emis.de/journals/JIS/VOL18/Szczyrba/sz3.pdf">Analytic Representations of the n-anacci Constants and Generalizations Thereof</a>, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.5.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1).
%F G.f.: (1+3*x-x^2)/(1-x-x^2-x^3).
%F a(n) = K(n) - 2*T(n+1) + 5*T(n), where K(n) = A001644(n) and T(n) = A000073(n+1). - _G. C. Greubel_, Apr 23 2019
%t LinearRecurrence[{1,1,1},{1,4,4},33] (* _Ray Chandler_, Dec 08 2013 *)
%o (PARI) my(x='x+O('x^40)); Vec((1+3*x-x^2)/(1-x-x^2-x^3)) \\ _G. C. Greubel_, Apr 23 2019
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+3*x-x^2)/(1-x-x^2-x^3) )); // _G. C. Greubel_, Apr 23 2019
%o (Sage) ((1+3*x-x^2)/(1-x-x^2-x^3)).series(x, 40).coefficients(x, sparse=False) # _G. C. Greubel_, Apr 23 2019
%o (GAP) a:=[1,4,4];; for n in [4..40] do a[n]:=a[n-1]+a[n-2]+a[n-3]; od; a; # _G. C. Greubel_, Apr 23 2019
%Y Cf. A000213, A000288, A000322, A000383, A060455, A136175, A141036, A141523, A214825-A214831.
%K nonn,easy
%O 0,2
%A _Abel Amene_, Jul 29 2012
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