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 A329244 #24 Apr 08 2024 12:47:53
%S A329244 1,2,3,5,10,22,50,115,266,617,1433,3330,7740,17992,41825,97230,226031,
%T A329244 525457,1221538,2839730,6601570,15346787,35676950,82938845,192809421,
%U A329244 448227522,1042002568,2422362080,5631308625,13091204282,30433357675,70748973085,164471408186
%N A329244 Sum of every third term of the Padovan sequence A000931.
%H A329244 Colin Barker, <a href="/A329244/b329244.txt">Table of n, a(n) for n = 0..1000</a>
%H A329244 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-5,3,-1).
%F A329244 a(n) = Sum_{i=0..n} A000931(3*i).
%F A329244 a(n) = A000931(3n+2)+1.
%F A329244 From _Colin Barker_, Nov 09 2019: (Start)
%F A329244 G.f.: (1 - 2*x) / ((1 - x)*(1 - 3*x + 2*x^2 - x^3)).
%F A329244 a(n) = 4*a(n-1) - 5*a(n-2) + 3*a(n-3) - a(n-4) for n>3. (End)
%e A329244 For n = 3, a(3) = 1+1+1+2 = 5.
%t A329244 LinearRecurrence[{4, -5, 3, -1}, {1, 2, 3, 5}, 50] (* _Paolo Xausa_, Apr 08 2024 *)
%o A329244 (Python)
%o A329244 p = lambda x:[1, 0, 0][x] if x<3 else p(x-2)+p(x-3)
%o A329244 a = lambda x:sum(p(3*i) for i in range(x+1))
%o A329244 (PARI) Vec((1 - 2*x) / ((1 - x)*(1 - 3*x + 2*x^2 - x^3)) + O(x^35)) \\ _Colin Barker_, Nov 09 2019
%Y A329244 Partial sums of A034943.
%Y A329244 Cf. A000931.
%K A329244 nonn,easy
%O A329244 0,2
%A A329244 _David Nacin_, Nov 09 2019