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 A383323 #16 May 02 2025 19:34:56
%S A383323 0,1,5,16,59,251,890,3270,12269,45793,167360,596036,2070755,7041087,
%T A383323 23517590,77417074,251879897,811815485,2596707692,8255064768,
%U A383323 26112370895,82260512731,258263585090,808543518254,2525239747781,7870664327961,24487769002520,76069664095420,235979863263419
%N A383323 Expansion of e.g.f. (1+x)*(exp(x)-1)*(exp(x)-x)*(exp(x)-x^2/2).
%C A383323 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 contain either one or no 3s.
%F A383323 a(n) = 3^(n-1)*(n+3) - 2^(n-3)*(3*binomial(n,3) + 6*binomial(n,2) + 8*n + 8) + 12*binomial(n,4) + 6*binomial(n,3) + 3*binomial(n,2) + n except at n = 3, 4.
%e A383323 a(3)=16 since the strings are: 011 (3 of this type), 002, (3 of this type), 003, (3 of this type), 023 (6 of this type) and 000.
%Y A383323 Cf. A358341.
%K A383323 nonn
%O A383323 0,3
%A A383323 _Enrique Navarrete_, Apr 23 2025