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 A038737 #38 Apr 24 2023 09:44:06
%S A038737 1,6,23,73,211,581,1560,4135,10890,28590,74946,196326,514123,1346148,
%T A038737 3524441,9227311,24157645,63245795,165579930,433494205,1134902916,
%U A038737 2971214796,7778741748,20365010748,53316290821,139583862066
%N A038737 T(n,n-2), array T as in A038792.
%C A038737 Fifth diagonal of array defined by T(i, 1)=T(1, j)=1, T(i, j)=Max(T(i-1, j)+T(i-1, j-1); T(i-1, j-1)+T(i, j-1)). - _Benoit Cloitre_, Aug 05 2003
%H A038737 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (6,-13,13,-6,1).
%F A038737 G.f.: x^2/((1-3*x+x^2)*(1-x)^3).
%F A038737 a(n) = Sum_{k=0..n} binomial(n+2,k+3)*Fibonacci(k). - _Vladimir Kruchinin_, Oct 24 2016
%F A038737 a(n) = Sum_{k=0..n} binomial(k+1,2)*Fibonacci(2*n-2*k). - _Greg Dresden_ and _Yu Xiao_, Jul 19 2020
%t A038737 Rest[Rest[CoefficientList[Series[x^2/((1-3*x+x^2)*(1-x)^3), {x, 0, 27}], x]]] (* _Georg Fischer_, Apr 15 2020 *)
%o A038737 (Maxima) a(n):=sum(binomial(n+2,k+3)*fib(k),k,0,n); /* _Vladimir Kruchinin_, Oct 24 2016 */
%o A038737 (Sage) [sum(binomial(k+1,2)*fibonacci(2*n-2*k) for k in (0..n)) for n in (2..27)] # _Stefano Spezia_, Apr 24 2023
%Y A038737 Apparently the same as A038797, but with offset 2.
%Y A038737 Cf. A038792.
%K A038737 nonn,easy
%O A038737 2,2
%A A038737 _Clark Kimberling_, May 02 2000