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 A113021 #19 Sep 08 2022 08:45:23
%S A113021 0,0,1,2,2,1,1,4,9,12,11,11,21,43,66,78,88,129,226,360,485,605,826,
%T A113021 1287,2012,2881,3851,5239,7669,11592,16936,23596,32581,46498,68366,
%U A113021 99913,142173,199384,282701,408720,593595,851835,1207901,1714447,2458522
%N A113021 Expansion of x^2/(1 - 2*x + 2*x^2 - x^3 - x^4).
%C A113021 Diagonal sums of number triangle A113020.
%H A113021 Matthew House, <a href="/A113021/b113021.txt">Table of n, a(n) for n = 0..6387</a>
%H A113021 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,-2,1,1).
%F A113021 a(n) = 2*a(n-1) - 2*a(n-2) + a(n-3) + a(n-4);
%F A113021 a(n) = Sum_{k=0..floor(n/2)} Sum_{j=0..n-k} C(n-k, j)*C(0, j-k)*Fibonacci(j-2k);
%F A113021 a(n) = Sum_{k=0..floor(n/2)} (-1)^(k+1)*binomial(n-k, k)*Fibonacci(k).
%t A113021 Table[Sum[(-1)^(k + 1) Binomial[n - k, k] Fibonacci@ k, {k, 0, Floor[n/2]}], {n, 0, 44}] (* _Michael De Vlieger_, Feb 13 2017 *)
%t A113021 LinearRecurrence[{2,-2,1,1},{0,0,1,2},50] (* _Harvey P. Dale_, Jul 16 2018 *)
%o A113021 (PARI) a(n)=([0,1,0,0; 0,0,1,0; 0,0,0,1; 1,1,-2,2]^n*[0;0;1;2])[1,1] \\ _Charles R Greathouse IV_, Feb 14 2017
%o A113021 (PARI) x='x+O('x^30); concat([0,0], Vec(x^2/(1-2*x+2*x^2-x^3-x^4))) \\ _G. C. Greubel_, Apr 09 2018
%o A113021 (Magma) I:=[0,0,1,2]; [n le 4 select I[n] else 2*Self(n-1) - 2*Self(n-2) + Self(n-3) + Self(n-4): n in [1..30]]; // _G. C. Greubel_, Apr 09 2018
%Y A113021 Cf. A096750, A113020.
%K A113021 easy,nonn
%O A113021 0,4
%A A113021 _Paul Barry_, Oct 11 2005