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 A141036 #48 Sep 08 2022 08:45:35
%S A141036 2,1,1,4,6,11,21,38,70,129,237,436,802,1475,2713,4990,9178,16881,
%T A141036 31049,57108,105038,193195,355341,653574,1202110,2211025,4066709,
%U A141036 7479844,13757578,25304131,46541553,85603262,157448946,289593761
%N A141036 Tribonacci-like sequence; a(0)=2, a(1)=1, a(2)=1, a(n) = a(n-1) + a(n-2) + a(n-3).
%C A141036 I used the short MATLAB program from the zip file link altered to produce a Lucas version of the tribonacci numbers.
%C A141036 No term is divisible by 8 or 9. - _Vladimir Joseph Stephan Orlovsky_, Mar 24 2011
%C A141036 a(A246517(n)) = A246518(n). - _Reinhard Zumkeller_, Sep 15 2014
%D A141036 Martin Gardner, Mathematical Circus, Random House, New York, 1981, p. 165.
%H A141036 Robert Price, <a href="/A141036/b141036.txt">Table of n, a(n) for n = 0..1000</a>
%H A141036 Martin Burtscher, Igor Szczyrba, Rafał Szczyrba, <a href="https://www.emis.de/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 A141036 T.-X. He, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL16/He/he13.html">Impulse Response Sequences and Construction of Number Sequence Identities</a>, J. Int. Seq. 16 (2013) #13.8.2
%H A141036 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1).
%F A141036 a(0)=2; a(1)=1; a(2)=1; a(n) = a(n-1) + a(n-2) + a(n-3).
%F A141036 From _R. J. Mathar_, Aug 04 2008: (Start)
%F A141036 a(n) = 2*A000213(n) - A000073(n+1).
%F A141036 O.g.f.: (2-x-2*x^2)/(1-x-x^2-x^3). (End)
%t A141036 a[0]=2; a[1]=1; a[2]=1; a[n_]:= a[n]=a[n-1]+a[n-2]+a[n-3]; Table[a[n], {n, 0, 40}] (* _Alonso del Arte_, Mar 24 2011 *)
%t A141036 LinearRecurrence[{1, 1, 1}, {2, 1, 1}, 40] (* _Vladimir Joseph Stephan Orlovsky_, Jul 22 2011 *)
%o A141036 (Haskell)
%o A141036 a141036 n = a141036_list !! n
%o A141036 a141036_list = 2 : 1 : 1 : zipWith3 (((+) .) . (+))
%o A141036 a141036_list (tail a141036_list) (drop 2 a141036_list)
%o A141036 -- _Reinhard Zumkeller_, Sep 15 2014
%o A141036 (PARI) a(n)=([0,1,0;0,0,1;1,1,1]^n*[2;1;1])[1,1] \\ _Charles R Greathouse IV_, Jun 15 2015
%o A141036 (PARI) my(x='x+O('x^40)); Vec((2-x-2*x^2)/(1-x-x^2-x^3)) \\ _G. C. Greubel_, Apr 22 2019
%o A141036 (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (2-x-2*x^2)/(1-x-x^2-x^3) )); // _G. C. Greubel_, Apr 22 2019
%o A141036 (Sage) ((2-x-2*x^2)/(1-x-x^2-x^3)).series(x, 41).coefficients(x, sparse=False) # _G. C. Greubel_, Apr 22 2019
%Y A141036 Cf. A000073, A000213, A001644 (Lucas tribonacci sequence), A246517, A246518.
%K A141036 nonn,easy
%O A141036 0,1
%A A141036 Matt Wynne (matwyn(AT)verizon.net), Jul 30 2008
%E A141036 Corrected offset and indices in formulas, _R. J. Mathar_, Aug 05 2008
%E A141036 Better name from _T. D. Noe_, Aug 06 2008