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 A384243 #11 May 27 2025 10:10:09
%S A384243 0,0,1,6,30,140,600,2352,8512,28800,92160,281600,827904,2356224,
%T A384243 6522880,17633280,46694400,121438208,310837248,784465920,1954938880,
%U A384243 4816896000,11747721216,28386000896,68010639360,161690419200,381681664000,895098028032,2086448136192,4836200284160
%N A384243 a(n) = 2^(n-6)*n*(n^3 - 6*n^2 + 19*n - 14).
%C A384243 a(n) is the number of strings of length n defined on {0, 1, 2, 3} that have exactly two 2's, zero or two 3's, and have no restriction on the number of 0's and 1's.
%H A384243 Paolo Xausa, <a href="/A384243/b384243.txt">Table of n, a(n) for n = 0..1000</a>
%H A384243 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (10,-40,80,-80,32).
%F A384243 E.g.f.: exp(2*x)*(x^2/2 + x^4/4).
%F A384243 G.f.: x^2*(1 - 4*x + 10*x^2)/(1 - 2*x)^5. - _Stefano Spezia_, May 23 2025
%e A384243 a(4) = 30 since the strings are the 6 permutations of 2233, the 6 permutations of 1122, the 6 permutations of 0022, and the 12 permutations of 0122.
%t A384243 A384243[n_] := 2^(n-6)*n*(n-1)*(n*(n-5)+14); Array[A384243, 30, 0] (* or *)
%t A384243 LinearRecurrence[{10, -40, 80, -80, 32}, {0, 0, 1, 6, 30}, 30] (* _Paolo Xausa_, May 27 2025 *)
%Y A384243 Cf. A060354, A327319, A383778.
%K A384243 nonn,easy
%O A384243 0,4
%A A384243 _Enrique Navarrete_, May 23 2025