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A244704 Number of n-node unlabeled rooted trees with thinning limbs and root outdegree (branching factor) 3. 2
1, 1, 3, 6, 13, 25, 55, 107, 224, 454, 938, 1916, 3969, 8163, 16918, 35010, 72724, 151093, 314749, 656115, 1370348, 2864948, 5998547, 12572884, 26385837, 55431031, 116577538, 245415158, 517152607, 1090771973, 2302729115, 4865449045, 10288826434, 21774842539 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,3

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 = 4..1000

FORMULA

a(n) ~ c * d^n / n^(3/2), where d = 2.1991393868..., c = 1.0259536... . - Vaclav Kotesovec, Aug 27 2014

EXAMPLE

a(7) = 6:

    o       o        o      o        o       o

   /|\     /|\      /|\    /|\     / | \    /|\

  o o o   o o o    o o o  o o o   o  o  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,

      `if`(n=v, 1, add(binomial(A(i, min(i-1, h))+j-1, 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, 3$2):

seq(a(n), n=4..50);

CROSSREFS

Column k=3 of A244657.

Sequence in context: A121349 A215984 A074890 * A032198 A079941 A255125

Adjacent sequences:  A244701 A244702 A244703 * A244705 A244706 A244707

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jul 04 2014

STATUS

approved

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Last modified November 16 06:50 EST 2018. Contains 317258 sequences. (Running on oeis4.)