|
|
A000235
|
|
Number of n-node rooted trees of height 3.
(Formerly M2732 N1097)
|
|
16
|
|
|
0, 0, 0, 1, 3, 8, 18, 38, 76, 147, 277, 509, 924, 1648, 2912, 5088, 8823, 15170, 25935, 44042, 74427, 125112, 209411, 348960, 579326, 958077, 1579098, 2593903, 4247768, 6935070, 11290627, 18330973, 29684082, 47946852, 77258764, 124198083
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,5
|
|
COMMENTS
|
(1, 1, 2, 3, 5, 8, ...) convolved with (0, 0, 1, 2, 4, 7, ...) = (0, 0, 1, 3, 8, ...). - Gary W. Adamson, Aug 14 2010
|
|
REFERENCES
|
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
LINKS
|
|
|
FORMULA
|
|
|
MAPLE
|
# For Maple program see link.
with(combstruct):
ZL:= proc(m) local i; [T0, {seq(T||i=Prod(Z, Set(T||(i+1))), i=0..m-1), T||m=Z}, unlabeled] end: A000235:= n-> count(ZL(3), size=n)-count(ZL(2), size=n): seq(A000235(n), n=1..36); # Zerinvary Lajos, Sep 23 2007
|
|
MATHEMATICA
|
m = 36; Rest @ CoefficientList[ Series[x*Product[(1-x^k)^(-PartitionsP[k-1]), {k, 1, m}], {x, 0, m}], x] - PartitionsP[Range[0, m-1]] (* Jean-François Alcover, Jul 05 2011, after Christian G. Bower *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|