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Number of homeomorphically irreducible leaf colored trees with n leaves using exactly 3 colors.
3

%I #8 Jan 10 2021 02:13:42

%S 0,0,1,9,63,412,2673,17571,117365,798819,5530122,38908380,277750749,

%T 2009160864,14707923021,108835512411,813241695330,6130521151377,

%U 46584949832013,356571373433217,2747371943624943,21296479544449677,165994877608025730,1300408539157086640

%N Number of homeomorphically irreducible leaf colored trees with n leaves using exactly 3 colors.

%H Andrew Howroyd, <a href="/A339786/b339786.txt">Table of n, a(n) for n = 1..500</a>

%F a(n) = A339783(n) - 3*A339782(n) + 3*A007827(n).

%o (PARI) my(N=25); (U(N,3) - 3*U(N,2) + 3*U(N,1))[2..1+N] \\ See A339780 for U(n, k).

%Y Column k=3 of A339780.

%Y Cf. A007827, A339782, A339783, A339785.

%K nonn

%O 1,4

%A _Andrew Howroyd_, Dec 18 2020