%I #32 Jul 27 2015 07:57:48

%S 0,0,0,0,0,3,9,23,65,186,507,1380,3764,10270,28001,76568,209749,

%T 575900,1584769,4371279,12083764,33477190,92939305,258537475,

%U 720575302,2012021934,5627886815,15768237664,44249863373,124365487416,350038837208,986579529425

%N Number of unlabeled rooted trees with n nodes where the outdegrees (branching factors) of at least one pair of adjacent nodes differ by at least two and the outdegrees of at least one pair of adjacent nodes are equal.

%H Alois P. Heinz, <a href="/A253244/b253244.txt">Table of n, a(n) for n = 0..400</a>

%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>

%H <a href="/index/Tra#trees">Index entries for sequences related to trees</a>

%F a(n) = A000081(n) - A260353(n) - A260403(n) + A257654(n).

%e a(5) = 3:

%e : o o o

%e : | / \ / \

%e : o o o o o

%e : | | / \

%e : o o o o

%e : / \ |

%e : o o o

%Y Cf. A000081, A260353, A260403, A257654.

%K nonn

%O 0,6

%A _Alois P. Heinz_, Jul 26 2015