|
Search: id:A003214
|
|
|
| A003214 |
|
Number of binary forests with n nodes.
(Formerly M0775)
|
|
+0
3
|
|
| 1, 1, 2, 3, 6, 10, 20, 37, 76, 152, 320, 672, 1454, 3154, 6959, 15439, 34608, 77988, 176985, 403510, 924683, 2127335, 4913452, 11385955, 26468231, 61700232, 144206269, 337837221, 793213550, 1866181155, 4398867672, 10387045476, 24567374217, 58196129468, 138056734916
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
From Piet Hut, Nov 07, 2003: "Number of ways to place n stars in stable hierarchical multiple star systems (where each stable multiple is a binary tree: around its center of mass two multiple star systems revolve, each of which can be a singleton or a nontrivial multiple star system).
"For example, a(1) = 1 : *; a(2) = 2 : (**), * *; a(3) = 3 : ((**)*), (**) *, * * *; a(4) = 6 : (((**)*)*), ((**)(**)), ((**)*) *, (**) (**), (**) * *, * * * * ."
|
|
REFERENCES
|
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
L. F. Meyers, Corrections and additions to Tree Representations in Linguistics. Report 3, 1966, p. 138. Project on Linguistic Analysis, Ohio State University Research Foundation, Columbus, Ohio.
L. F. Meyers and W. S.-Y. Wang, Tree Representations in Linguistics. Report 3, 1963, pp. 107-108. Project on Linguistic Analysis, Ohio State University Research Foundation, Columbus, Ohio.
|
|
LINKS
|
T. D. Noe, Table of n, a(n) for n=0..200
Piet Hut, Home Page
|
|
FORMULA
|
Euler transform of A001190. - Michael Somos, Nov 10 2003
G.f.: exp( sum G001190(x^i)/i, i=1..infinity ), where G001190 = g.f. for A001190.
|
|
CROSSREFS
|
Cf. A001190.
Adjacent sequences: A003211 A003212 A003213 this_sequence A003215 A003216 A003217
Sequence in context: A045690 A007148 A093371 this_sequence A123423 A005195 A052843
|
|
KEYWORD
|
nonn,easy,nice
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
Search completed in 0.002 seconds
|
