A245123 Number of n-node rooted identity trees with thinning limbs and root outdegree (branching factor) 4.

2, 3, 9, 20, 46, 94, 202, 412, 850, 1719, 3483, 6987, 14026, 27990, 55830, 111022, 220589, 437451, 866898, 1715821, 3393973, 6708016, 13251455, 26163174, 51635765, 101868226, 200908954, 396129137, 780868821, 1538971204, 3032575428, 5974874666, 11770477038

Offset

11,1

Links

Alois P. Heinz, Table of n, a(n) for n = 11..1000

Example

a(11) = 2:
:     o          o      :
:   /( )\     / ( ) \   :
:  o o o o   o  o o  o  :
:  | | |    ( ) | |     :
:  o o o    o o o o     :
:  | |      |   |       :
:  o o      o   o       :
:  |                    :
:  o                    :

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, add(binomial(A(i, min(i-1, h)), j)
       *b(n-i*j, i-1, h, v-j), j=0..min(n/i, v))))
    end:
A:= proc(n, k) option remember;
      `if`(n<2, n, add(b(n-1$2, j$2), j=1..min(k, n-1)))
    end:
a:= n-> b(n-1$2, 4$2):
seq(a(n), n=11..50);

Crossrefs

Column k=4 of A245120.

Sequence in context: A121908 A231368 A369517 * A097075 A036673 A111189

Adjacent sequences: A245120 A245121 A245122 * A245124 A245125 A245126

Keyword

nonn

Author

Alois P. Heinz, Jul 12 2014

Status

approved