|
| |
|
|
A004113
|
|
Number of rooted trees with n nodes and 2-colored non-leaf nodes.
(Formerly M1629)
|
|
4
| |
|
|
1, 2, 6, 18, 60, 204, 734, 2694, 10162, 38982, 151920, 599244, 2389028, 9608668, 38945230, 158904230, 652178206, 2690598570, 11151718166, 46412717826, 193891596436, 812748036380, 3417407089470, 14410094628558, 60920843101858, 258169745573158, 1096494947168142
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
REFERENCES
| F. Harary, R. W. Robinson and A. J. Schwenk, Twenty-step algorithm for determining the asymptotic number of trees of various species, J. Austral. Math. Soc., Series A, 20 (1975), 483-503. Errata: Vol. A 41 (1986), p. 325.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
|
LINKS
| N. J. A. Sloane, Transforms
Index entries for sequences related to rooted trees
Index entries for sequences related to trees
|
|
|
FORMULA
| Shifts left and halves under EULER transform.
|
|
|
MAPLE
| with (numtheory): etr:= proc(p) local b; b:= proc(n) option remember; `if` (n=0, 1, (add (add(d*p(d), d=divisors(j)) *b(n-j), j=1..n))/n) end end: b:= etr(a): a:= n-> `if` (n<=1, n, 2*b(n-1)): seq (a(n), n=1..30); # Alois P. Heinz, Sep 06 2008
|
|
|
CROSSREFS
| Cf. A004114, A052316, A052317.
Sequence in context: A150043 A048117 A048118 * A150044 A108531 A150045
Adjacent sequences: A004110 A004111 A004112 * A004114 A004115 A004116
|
|
|
KEYWORD
| nonn,eigen
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| Extended with better description from Christian G. Bower (bowerc(AT)usa.net), Apr 15 1998.
|
| |
|
|
