

A244705


Number of nnode unlabeled rooted trees with thinning limbs and root outdegree (branching factor) 4.


2



1, 1, 3, 6, 15, 29, 68, 140, 312, 660, 1443, 3084, 6710, 14425, 31278, 67508, 146300, 316424, 685955, 1486008, 3223480, 6992012, 15179437, 32960891, 71617874, 155661971, 338508703, 736401503, 1602712182, 3489454243, 7600403101, 16560519877, 36097320801
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OFFSET

5,3


COMMENTS

In a rooted tree with thinning limbs the outdegree of a parent node is larger than or equal to the outdegree of any of its child nodes.


LINKS

Alois P. Heinz, Table of n, a(n) for n = 5..1000


MAPLE

b:= proc(n, i, h, v) option remember; `if`(n=0,
`if`(v=0, 1, 0), `if`(i<1 or v<1 or n<v, 0,
`if`(n=v, 1, add(binomial(A(i, min(i1, h))+j1, j)
*b(ni*j, i1, h, vj), j=0..min(n/i, v)))))
end:
A:= proc(n, k) option remember;
`if`(n<2, n, add(b(n1$2, j$2), j=1..min(k, n1)))
end:
a:= n> b(n1$2, 4$2):
seq(a(n), n=5..50);


CROSSREFS

Column k=4 of A244657.
Sequence in context: A034464 A116696 A000220 * A319643 A092641 A077449
Adjacent sequences: A244702 A244703 A244704 * A244706 A244707 A244708


KEYWORD

nonn


AUTHOR

Alois P. Heinz, Jul 04 2014


STATUS

approved



