PROG
(MAGMAMagma) I:=[3, 1, 1]; [n le 3 select I[n] else Self(n-1)+Self(n-2) +Self(n-3): n in [1..40]]; // Vincenzo Librandi, Oct 17 2012
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(MAGMAMagma) I:=[3, 1, 1]; [n le 3 select I[n] else Self(n-1)+Self(n-2) +Self(n-3): n in [1..40]]; // Vincenzo Librandi, Oct 17 2012
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Martin Burtscher, Igor Szczyrba, Rafał Szczyrba, <a href="httphttps://www.emis.de/journals/JIS/VOL18/Szczyrba/sz3.pdfhtml">Analytic Representations of the n-anacci Constants and Generalizations Thereof</a>, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.5.
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<a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1).
a(0)=3; a(1)=1; a(2)=1; thereafter a(n) = a(n-1) + a(n-2) + a(n-3).
From R. J. Mathar, Aug 22 2008: (Start)
O.g.f.: (3-2*x-3*x^2)/(1-x-x^2-x^3). a(n)= A001644(n) - 2*A000073(n). - _R. J. Mathar_, Aug 22 2008
Clear[f, g, n, a] a[0] = 3; a[1] = 1; a[2] = 1; a[n_] := a[n] = a[n - 1] + a[n - 2] + a[n - 3]; Table[a[n], {n, 0, 3040}]
(MAGMA) I:=[3, 1, 1]; [n le 3 select I[n] else Self(n-1)+Self(n-2) +Self(n-3): n in [1..40]]; // Vincenzo Librandi, Oct 17 2012
(PARI) my(x='x+O('x^40)); Vec((3-2*x-3*x^2)/(1-x-x^2-x^3)) \\ G. C. Greubel, Apr 22 2019
(Sage) ((3-2*x-3*x^2)/(1-x-x^2-x^3)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Apr 22 2019
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(PARI) a(n)=([0, 1, 0; 0, 0, 1; 1, 1, 1]^n*[3; 1; 1])[1, 1] \\ Charles R Greathouse IV, Mar 22 2016
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<a href="/index/Rec">Index to sequences with entries for linear recurrences with constant coefficients</a>, signature (1,1,1).
<a href="/index/Rec#recLCC">Index to sequences with linear recurrences with constant coefficients</a>, signature (1,1,1).