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 A047081 #19 Mar 28 2025 06:48:39
%S A047081 1,2,3,6,11,20,37,68,125,230,423,778,1431,2632,4841,8904,16377,30122,
%T A047081 55403,101902,187427,344732,634061,1166220,2145013,3945294,7256527,
%U A047081 13346834,24548655,45152016,83047505,152748176,280947697,516743378,950439251,1748130326,3215312955,5913882532,10877325813
%N A047081 a(n) = Sum_{k=0..n} T(n, k), array T as in A047080.
%H A047081 G. C. Greubel, <a href="/A047081/b047081.txt">Table of n, a(n) for n = 0..1000</a>
%H A047081 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1).
%F A047081 From _G. C. Greubel_, Oct 31 2022: (Start)
%F A047081 G.f.: (1 + x)/(1 - x - x^2 - x^3).
%F A047081 a(n) = A000073(n+1) + A000073(n+2). (End)
%F A047081 a(n) = Sum_{r root of x^3-x^2-x-1} r^n/(-3*r^2+5*r+2). - _Fabian Pereyra_, Nov 23 2024
%F A047081 a(n) = A001590(n+3). - _R. J. Mathar_, Mar 28 2025
%t A047081 LinearRecurrence[{1,1,1}, {1,2,3}, 61] (* _G. C. Greubel_, Oct 31 2022 *)
%o A047081 (Magma) [n le 3 select n else Self(n-1) +Self(n-2) +Self(n-3): n in [1..60]]; // _G. C. Greubel_, Oct 31 2022
%o A047081 (SageMath)
%o A047081 @CachedFunction
%o A047081 def a(n): return (n+1) if (n<3) else a(n-1) +a(n-2) +a(n-3) # a = A047081
%o A047081 [a(n) for n in (0..60)] # _G. C. Greubel_, Oct 31 2022
%Y A047081 Cf. A047080, A047082, A047083, A047084, A047085, A047086, A047087, A047088.
%Y A047081 Cf. A000073, A254006.
%K A047081 easy,nonn
%O A047081 0,2
%A A047081 _Clark Kimberling_
%E A047081 Data corrected by _G. C. Greubel_, Oct 31 2022