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 A387604 #20 Sep 03 2025 13:10:00
%S A387604 1,6,27,114,495,2214,9990,44982,201933,905526,4061016,18217710,
%T A387604 81735156,366712272,1645244379,7381235808,33115172733,148568241906,
%U A387604 666539094105,2990373257970,13416063062094,60190050847500,270037644213267,1211501390490972,5435300133382176
%N A387604 a(n) = (1/2) * Sum_{k=0..floor(n/3)} 3^(n-2*k) * binomial(2*n-4*k+2,2*k+1).
%H A387604 Vincenzo Librandi, <a href="/A387604/b387604.txt">Table of n, a(n) for n = 0..1000</a>
%H A387604 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-9,6,18,0,-9).
%F A387604 G.f.: B(x)^2, where B(x) is the g.f. of A387513.
%F A387604 G.f.: 1/((1-3*x-3*x^3)^2 - 36*x^4).
%F A387604 a(n) = 6*a(n-1) - 9*a(n-2) + 6*a(n-3) + 18*a(n-4) - 9*a(n-6).
%t A387604 Table[Sum[3^(n-2*k)*Binomial[2*n-4*k+2, 2*k+1]/2,{k,0,Floor[n/3]}],{n,0,40}] (* _Vincenzo Librandi_, Sep 03 2025 *)
%o A387604 (PARI) a(n) = sum(k=0, n\3, 3^(n-2*k)*binomial(2*n-4*k+2, 2*k+1))/2;
%o A387604 (Magma) [&+[3^(n-2*k)* Binomial(2*n-4*k+2, 2*k+1)/2: k in [0..Floor (n/3)]]: n in [0..35]]; // _Vincenzo Librandi_, Sep 03 2025
%Y A387604 Cf. A375278, A387602.
%Y A387604 Cf. A387513.
%K A387604 nonn,easy,new
%O A387604 0,2
%A A387604 _Seiichi Manyama_, Sep 02 2025