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 A383409 #9 May 02 2025 19:35:20
%S A383409 0,1,5,19,77,326,1406,5601,23715,101092,431172,1841357,7889877,
%T A383409 33924268,146103678,628595097,2695143751,11495831852,48733234456,
%U A383409 205252231229,858955851705,3573016550756,14781047390930,60846099935609,249385924540907
%N A383409 Expansion of e.g.f. (exp(x)-1)*(exp(x)-x)*(exp(x)-x^2/2)*(exp(x)-x^3/6).
%C A383409 a(n) is the number of strings of length n defined on {0, 1, 2, 3} that contain at least one 0, do not contain exactly one 1, do not contain exactly two 2s, and do not contain exactly three 3s.
%F A383409 a(n) = 4^n - 3^n - n*(3^(n-1) - 2^(n-1)) - binomial(n,2)*(3^(n-2) - 2^(n-2)) - binomial(n,3)*(3^(n-3) - 2^(n-1) + 3) + binomial(n,4)*(2^(n-2) - 4) + 5*binomial(n,5)*(2^(n-4) - 2) - 60*binomial(n,6) except at n = 6.
%e A383409 a(3)=19 since the strings are: 011 (3 of this type), 033 (3 of this type), 002 (3 of this type), 003 (3 of this type), 023 (6 of this type), and 000.
%Y A383409 Cf. A383323.
%K A383409 nonn
%O A383409 0,3
%A A383409 _Enrique Navarrete_, Apr 26 2025