login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A001860 Number of series-reduced planted trees with n+9 nodes and 4 internal nodes.
(Formerly M2917 N1171)
1
0, 3, 12, 29, 57, 99, 157, 234, 333, 456, 606, 786, 998, 1245, 1530, 1855, 2223, 2637, 3099, 3612, 4179, 4802, 5484, 6228, 7036, 7911, 8856, 9873, 10965, 12135, 13385, 14718, 16137, 17644, 19242, 20934, 22722, 24609, 26598, 28691, 30891, 33201, 35623, 38160 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.

John Riordan, personal communication.

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

T. D. Noe, Table of n, a(n) for n = 0..1000

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.

Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992.

Index entries for sequences related to rooted trees

Index entries for sequences related to trees

FORMULA

G.f.: x*(3 + 3*x + 2*x^2)/((1-x)^3*(1-x^3)).

[(8*n^3 + 27*n^2 + 21*n + 9)/18]

EXAMPLE

Examples for n=1 (i=internal, e=external node):

............................................e...e

...........e.e...........e.e.e.e..........e...i..

.......e.e..i...e.........i...i.........e...i....

........i.....i.........e...i.........e...i......

...........i..............i.............i........

...........e..............e.............e........

MAPLE

A001860:=(3+3*z+2*z**2)/(z**2+z+1)/(z-1)**4; # conjectured by Simon Plouffe in his 1992 dissertation

MATHEMATICA

nn = 50; CoefficientList[Series[x*(3 + 3*x + 2*x^2)/((1 - x)^3*(1 - x^3)), {x, 0, nn}], x] (* T. D. Noe, Aug 10 2012 *)

PROG

(PARI) a(n)=(8*n^3+27*n^2+21*n+9)\18

CROSSREFS

Sequence in context: A124052 A215640 A104353 * A199035 A101459 A051408

Adjacent sequences:  A001857 A001858 A001859 * A001861 A001862 A001863

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

Additional comments from Michael Somos, Jun 06 2002

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified February 23 02:43 EST 2018. Contains 299473 sequences. (Running on oeis4.)