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 A387625 #16 Sep 05 2025 11:34:04
%S A387625 1,1,1,7,21,43,93,251,661,1587,3805,9499,23813,58691,144141,356491,
%T A387625 883637,2184115,5391869,13325371,32953317,81459235,201299565,
%U A387625 497518187,1229819541,3039854611,7513347421,18570354203,45900859333,113454099843,280422868685
%N A387625 a(n) = Sum_{k=0..floor(n/3)} 2^k * binomial(2*n-4*k+1,2*k).
%H A387625 Vincenzo Librandi, <a href="/A387625/b387625.txt">Table of n, a(n) for n = 0..1000</a>
%H A387625 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,4,4,0,-4).
%F A387625 G.f.: (1-x+2*x^3)/((1-x+2*x^3)^2 - 8*x^3).
%F A387625 a(n) = 2*a(n-1) - a(n-2) + 4*a(n-3) + 4*a(n-4) - 4*a(n-6).
%t A387625 Table[Sum[2^k*Binomial[2*n-4*k+1,2*k],{k,0,Floor[n/3]}],{n,0,40}] (* _Vincenzo Librandi_, Sep 04 2025 *)
%o A387625 (PARI) a(n) = sum(k=0, n\3, 2^k*binomial(2*n-4*k+1, 2*k));
%o A387625 (Magma) [&+[2^k* Binomial(2*n-4*k+1, 2*k): k in [0..Floor (n/3)]]: n in [0..30]]; // _Vincenzo Librandi_, Sep 04 2025
%Y A387625 Cf. A002315, A387624, A387626.
%K A387625 nonn,easy,new
%O A387625 0,4
%A A387625 _Seiichi Manyama_, Sep 03 2025