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 A383868 #10 May 18 2025 18:40:12
%S A383868 1,2,6,20,70,252,904,3152,10560,33920,104704,311808,899584,2524160,
%T A383868 6912000,18526208,48726016,126025728,321126400,807403520,2005794816,
%U A383868 4929093632,11994136576,28924968960,69185044480,164240556032,387201368064,907009851392,2112083722240
%N A383868 a(n) = 2^(n-3)*(3*binomial(n,4) + 4*binomial(n,2) + 8).
%C A383868 a(n) is the number of strings of length n defined on {0,1,2,3} that contain zero or two 2s, zero or two 3s, and have no restriction on the number of 0s and 1s.
%H A383868 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (10,-40,80,-80,32).
%F A383868 E.g.f.: exp(2*x)*(1+x^2/2)^2.
%F A383868 G.f.: (1 - 8*x + 26*x^2 - 40*x^3 + 30*x^4)/(1 - 2*x)^5. - _Stefano Spezia_, May 13 2025
%e A383868 a(2) = 6 since the strings are 01, 10, 00, 11, 22, and 33.
%t A383868 a[n_] := 2^(n-3) * (3*Binomial[n, 4] + 4*Binomial[n, 2] + 8); Array[a, 30, 0] (* _Amiram Eldar_, May 13 2025 *)
%Y A383868 Cf. A383778.
%K A383868 nonn,easy
%O A383868 0,2
%A A383868 _Enrique Navarrete_, May 12 2025