login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A000550 Number of trees of diameter 7.
(Formerly M2969 N1201)
3
1, 3, 14, 42, 128, 334, 850, 2010, 4625, 10201, 21990, 46108, 94912, 191562, 380933, 746338, 1444676, 2763931, 5235309, 9822686, 18275648, 33734658, 61826344, 112550305, 203627610, 366267931, 655261559, 1166312530, 2066048261, 3643352362, 6397485909, 11188129665, 19491131627, 33831897511, 58519577756, 100885389220, 173368983090, 297021470421, 507378371670, 864277569606, 1468245046383, 2487774321958, 4204663810414, 7089200255686, 11924621337321, 20012746962064, 33513139512868, 56001473574091, 93387290773141, 155419866337746 (list; graph; refs; listen; history; text; internal format)
OFFSET

8,2

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

Alois P. Heinz, Table of n, a(n) for n = 8..2500

J. Riordan, Enumeration of trees by height and diameter, IBM J. Res. Dev. 4 (1960), 473-478.

Index entries for sequences related to trees

FORMULA

G.f.: a(x)=(r(x)^2+r(x^2))/2, where r(x) is the generating function of A000235. - Sean A. Irvine, Nov 21 2010

MAPLE

b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1 or k<1, 0,

     add(binomial(b((i-1)$2, k-1)+j-1, j)*b(n-i*j, i-1, k), j=0..n/i)))

    end:

g:= n-> b((n-1)$2, 3) -b((n-1)$2, 2):

a:= n-> (add(g(i)*g(n-i), i=0..n)+`if`(n::even, g(n/2), 0))/2:

seq(a(n), n=8..40);  # Alois P. Heinz, Feb 09 2016

MATHEMATICA

m = 50; r[x_] = (Rest @ CoefficientList[ Series[ x*Product[ (1 - x^k)^(- PartitionsP[k-1]), {k, 1, m+3}], {x, 0, m+3}], x] - PartitionsP[ Range[0, m+2]]).(x^Range[m+3]); A000550 = CoefficientList[(r[x]^2 + r[x^2])/2, x][[9 ;; m+8]] (* Jean-Fran├žois Alcover, Feb 09 2016 *)

CROSSREFS

Cf. A034853, A000306 (diameter 8)

Sequence in context: A296267 A104905 A055650 * A124650 A291138 A063903

Adjacent sequences:  A000547 A000548 A000549 * A000551 A000552 A000553

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Sean A. Irvine, Nov 21 2010

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 27 13:00 EDT 2020. Contains 334657 sequences. (Running on oeis4.)