This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A214828 #33 Jun 15 2025 23:58:29
%S A214828 1,6,6,13,25,44,82,151,277,510,938,1725,3173,5836,10734,19743,36313,
%T A214828 66790,122846,225949,415585,764380,1405914,2585879,4756173,8747966,
%U A214828 16090018,29594157,54432141,100116316,184142614,338691071,622950001
%N A214828 a(n) = a(n-1) + a(n-2) + a(n-3), with a(0) = 1, a(1) = a(2) = 6.
%C A214828 See comments in A214727.
%H A214828 Robert Price, <a href="/A214828/b214828.txt">Table of n, a(n) for n = 0..1000</a>
%H A214828 Martin Burtscher, Igor Szczyrba, and Rafał Szczyrba, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL18/Szczyrba/sz3.html">Analytic Representations of the n-anacci Constants and Generalizations Thereof</a>, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.5.
%H A214828 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1).
%F A214828 G.f.: (1+5*x-x^2)/(1-x-x^2-x^3).
%F A214828 a(n) = -A000073(n) + 5*A000073(n+1) + A000073(n+2). - _G. C. Greubel_, Apr 24 2019
%t A214828 LinearRecurrence[{1,1,1},{1,6,6},33] (* _Ray Chandler_, Dec 08 2013 *)
%o A214828 (PARI) my(x='x+O('x^40)); Vec((1+5*x-x^2)/(1-x-x^2-x^3)) \\ _G. C. Greubel_, Apr 24 2019
%o A214828 (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+5*x-x^2)/(1-x-x^2-x^3) )); // _G. C. Greubel_, Apr 24 2019
%o A214828 (Sage) ((1+5*x-x^2)/(1-x-x^2-x^3)).series(x, 40).coefficients(x, sparse=False) # _G. C. Greubel_, Apr 24 2019
%o A214828 (GAP) a:=[1,6,6];; 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 A214828 Cf. A000213, A000288, A000322, A000383, A060455, A136175, A141036, A141523, A214825-A214831.
%K A214828 nonn,easy
%O A214828 0,2
%A A214828 _Abel Amene_, Jul 30 2012