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Number of homeomorphically irreducible leaf colored trees with n leaves using exactly 4 colors.
2

%I #8 Jan 10 2021 02:13:45

%S 0,0,0,4,68,812,8512,84312,814184,7781712,74182124,708344640,

%T 6790655496,65440865012,634347822304,6186652422650,60707391493004,

%U 599283097168488,5950282272766412,59408426130151164,596269843123151304,6014472189177940224,60952019560703982452

%N Number of homeomorphically irreducible leaf colored trees with n leaves using exactly 4 colors.

%H Andrew Howroyd, <a href="/A339787/b339787.txt">Table of n, a(n) for n = 1..500</a>

%e There are 2 homeomorphically reduced trees with 4 leafs:

%e o o o

%e | | |

%e o---o---o o---o

%e | | |

%e o o o

%e The leaves of the first tree can be colored in 1 way using all four colors and the second can be colored in 3 ways, so a(4) = 1 + 3 = 4.

%o (PARI) my(N=25); M(N,4)[2..1+N, 5]~ \\ See A339780 for M(n, m).

%Y Column k=4 of A339780.

%Y Cf. A339785, A339786.

%K nonn

%O 1,4

%A _Andrew Howroyd_, Dec 18 2020