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 A387652 #15 Sep 05 2025 14:46:53
%S A387652 1,0,0,3,2,0,5,20,4,7,70,84,17,168,504,299,346,1848,2653,1452,5180,
%T A387652 13743,12350,14508,51561,81440,68432,162323,391026,442544,555445,
%U A387652 1498116,2500276,2666711,5202550,11465284,14985153,20025432,45011176,77173371,95454666,168802152
%N A387652 a(n) = Sum_{k=0..floor(n/3)} 2^(n-3*k) * binomial(2*k+1,2*n-6*k+1).
%H A387652 Vincenzo Librandi, <a href="/A387652/b387652.txt">Table of n, a(n) for n = 0..1500</a>
%H A387652 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,2,4,0,-1,4,-4).
%F A387652 G.f.: (1+x^3-2*x^4)/((1+x^3-2*x^4)^2 - 4*x^3).
%F A387652 a(n) = 2*a(n-3) + 4*a(n-4) - a(n-6) + 4*a(n-7) - 4*a(n-8).
%t A387652 Table[Sum[2^(n-3*k)*Binomial[2*k+1,2*n-6*k+1],{k,0,Floor[n/3]}],{n,0,40}] (* _Vincenzo Librandi_, Sep 05 2025 *)
%o A387652 (PARI) a(n) = sum(k=0, n\3, 2^(n-3*k)*binomial(2*k+1, 2*n-6*k+1));
%o A387652 (Magma) [&+[2^(n-3*k)* Binomial(2*k+1, 2*n-6*k+1): k in [0..Floor (n/3)]]: n in [0..40]]; // _Vincenzo Librandi_, Sep 05 2025
%Y A387652 Cf. A387627, A387651.
%Y A387652 Cf. A387648.
%K A387652 nonn,new
%O A387652 0,4
%A A387652 _Seiichi Manyama_, Sep 05 2025