OFFSET
0,2
COMMENTS
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.
LINKS
Paolo Xausa, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (10,-33,36).
FORMULA
E.g.f.: exp(3*x)*(exp(x)-x).
From Alois P. Heinz, Jan 29 2025: (Start)
G.f.: -(13*x^2-7*x+1)/((4*x-1)*(3*x-1)^2).
EXAMPLE
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.
MATHEMATICA
Table[4^n - n*3^(n - 1), {n, 0, 25}] (* Paolo Xausa, Feb 06 2025 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Enrique Navarrete, Jan 29 2025
STATUS
approved