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 A383778 #8 May 14 2025 18:52:33
%S A383778 0,1,4,15,56,200,672,2128,6400,18432,51200,137984,362496,931840,
%T A383778 2351104,5836800,14286848,34537472,82575360,195493888,458752000,
%U A383778 1067974656,2468347904,5667553280,12935233536,29360128000,66303557632,149032009728,333531054080,743431995392
%N A383778 a(n) = n*(n^2 - 3*n + 10)*2^(n-4).
%C A383778 a(n) is the number of strings of length n defined on {0,1,2,3} that contain exactly one 3, zero or two 2s and have no restriction on the number of 0s and 1s.
%H A383778 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (8,-24,32,-16).
%F A383778 E.g.f.: x*(1 + x^2/2)*exp(2*x).
%F A383778 G.f.: x*(1 - 4*x + 7*x^2)/(1 - 2*x)^4. - _Stefano Spezia_, May 10 2025
%e A383778 a(3) = 15 since the strings are 322 (3 of this type), 300 (3 of this type), 311 (3 of this type), and 301 (6 of this type).
%t A383778 a[n_] := n*(n^2-3*n+10)*2^(n-4); Array[a, 30, 0] (* _Amiram Eldar_, May 09 2025 *)
%Y A383778 Cf. A060354.
%K A383778 nonn,easy
%O A383778 0,3
%A A383778 _Enrique Navarrete_, May 09 2025