OFFSET
0,2
COMMENTS
a(n) is the number of words of length n defined on 4 symbols where three chosen symbols (say, the three largest ones) are used at most twice.
LINKS
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
FORMULA
a(n) = 37 - 94*(n+1) + (187/2)*(n+1)^2 - (373/8)*(n+1)^3 + (103/8)*(n+1)^4 - (15/8)*(n+1)^5 + (1/8)*(n+1)^6.
E.g.f.: (1 + x + x^2/2)^3*exp(x).
G.f.: (1 - 3*x + 9*x^2 - 2*x^3 + 21*x^4 + 27*x^5 + 37*x^6)/(1 - x)^7. - Stefano Spezia, Apr 01 2025
EXAMPLE
a(3) = 61 since from the 64 words defined on {0, 1, 2, 3} we subtract the three words 111, 222, 333.
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Enrique Navarrete, Apr 01 2025
STATUS
approved