|
Search: id:A007827
|
|
|
| A007827 |
|
Number of homeomorphically irreducible (or series-reduced) trees with n pendant nodes, or continua with n non-cut points, or leaves. |
|
+0
6
|
|
| 1, 1, 1, 1, 2, 3, 7, 13, 32, 73, 190, 488, 1350, 3741, 10765, 31311, 92949, 278840, 847511, 2599071, 8044399, 25082609, 78758786, 248803504, 790411028, 2523668997, 8095146289, 26076714609, 84329102797, 273694746208
(list; graph; listen)
|
|
|
OFFSET
|
0,5
|
|
|
REFERENCES
|
M. Cropper, J. Combin. Math. Combin. Comp., Vol. 24 (1997), 177-184.
F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 62.
S. B. Nadler Jr., Continuum Theory, Academic Press.
|
|
LINKS
|
P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.
Index entries for sequences related to trees
Index entries for sequences related to rooted trees
|
|
FORMULA
|
G.f.: 1+(1+x-B(x))*B(x) where B(x) = x+x^2+2*x^3+5*x^4+12*x^5+33*x^6+90*x^7+... is g.f. for A000669.
|
|
MAPLE
|
A := series(1+(1+x-B)*B, x, 30); # where B = g.f. for A000669; A007827 := n->coeff(A, x, n);
|
|
CROSSREFS
|
Cf. A000014 (series-reduced trees), A000055 (trees), A000311, A000669 (series-reduced planted trees by leaves), A059123 (homeomorphically irreducible rooted trees by nodes)
Number of row entries of A064060.
Adjacent sequences: A007824 A007825 A007826 this_sequence A007828 A007829 A007830
Sequence in context: A002013 A003120 A032131 this_sequence A129859 A056953 A045611
|
|
KEYWORD
|
nonn,nice,easy
|
|
AUTHOR
|
Matthew Cropper (mmcrop01(AT)athena.louisville.edu).
|
|
EXTENSIONS
|
Corrected and extended by Christian G. Bower (bowerc(AT)usa.net), Nov 15 1999.
|
|
|
Search completed in 0.002 seconds
|
