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 A087635 #33 Apr 29 2025 04:43:19
%S A087635 0,2,12,64,336,1760,9216,48256,252672,1323008,6927360,36272128,
%T A087635 189923328,994451456,5207015424,27264286720,142757658624,747488804864,
%U A087635 3913902194688,20493457948672,107305138913280,561857001684992
%N A087635 a(n) = S(n,3) where S(n,m) = Sum_{k=0..n} binomial(n,k)*Fibonacci(m*k).
%H A087635 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,-4).
%F A087635 a(n) = 6*a(n-1)-4*a(n-2) = 2*A084326(n).
%F A087635 a(n) = Sum_{0<=j<=i<=n} C(i,j)*C(n,i)*Fibonacci(i+j). - _Benoit Cloitre_, May 21 2005
%F A087635 a(n) = 2^n*Fibonacci(2*n). - _Benoit Cloitre_, Sep 13 2005
%F A087635 a(n) = Sum_{k=0..n} C(n,k)*Fibonacci(k)*Lucas(n-k). - _Ross La Haye_, Aug 14 2006
%F A087635 G.f.: 2*x/(1-6*x+4*x^2). - _Colin Barker_, Jun 19 2012
%t A087635 LinearRecurrence[{6,-4}, {0, 2}, 22] (* _Amiram Eldar_, Apr 29 2025 *)
%Y A087635 Cf. A000045, A001906 (S(n, 1)), A030191 (S(n, 2)).
%Y A087635 Cf. A084326.
%K A087635 nonn,easy
%O A087635 0,2
%A A087635 _Benoit Cloitre_, Oct 23 2003