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 A380651 #31 Feb 06 2025 08:21:54
%S A380651 1,3,10,37,148,619,2638,11281,48040,203095,851746,3544765,14651452,
%T A380651 60200131,246114934,1001997289,4065384784,16448074927,66394953802,
%U A380651 267516917653,1076266398436,4324824038683,17362058273950,69646979806657,279215540418808
%N A380651 a(n) = 4^n - n*3^(n-1).
%C A380651 a(n) is the number of words of length n defined on 4 letters where one of the letters is not used or is used any number of times except once.
%H A380651 Paolo Xausa, <a href="/A380651/b380651.txt">Table of n, a(n) for n = 0..1000</a>
%H A380651 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (10,-33,36).
%F A380651 E.g.f.: exp(3*x)*(exp(x)-x).
%F A380651 From _Alois P. Heinz_, Jan 29 2025: (Start)
%F A380651 G.f.: -(13*x^2-7*x+1)/((4*x-1)*(3*x-1)^2).
%F A380651 a(n) = A000302(n) - A027471(n+1). (End)
%e A380651 For n=2, the 10 words on {0, 1, 2, 3} that do not use 0 exactly once are 12, 21, 13, 31, 23, 32, 11, 22, 33, 00.
%t A380651 Table[4^n - n*3^(n - 1), {n, 0, 25}] (* _Paolo Xausa_, Feb 06 2025 *)
%Y A380651 Cf. A000302, A027471.
%K A380651 nonn,easy
%O A380651 0,2
%A A380651 _Enrique Navarrete_, Jan 29 2025