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!)
A095338 Total number of leaves in the labeled graphs of order n. 3
0, 2, 12, 96, 1280, 30720, 1376256, 117440512, 19327352832, 6184752906240, 3870280929771520, 4755801206503243776, 11510768301994760208384, 55006124792465627449131008, 519934816499859715457632174080, 9735556609752801803494680617287680, 361550014853497117429835520396253724672 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A leaf is defined as a vertex of degree (or valence) 1. - Michael Somos, Mar 13 2014

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..80

Eric Weisstein's World of Mathematics, Tree Leaf

FORMULA

Conjecture: a(n) = n*(n-1)*2^binomial(n-1,2). - Vladeta Jovovic, Jan 26 2006

a(n) = n*(n-1)*2^binomial(n-1,2) is correct, since counting the total number of leaves in the labeled graphs of order n is equivalent to counting all labeled rooted graphs of order n where the root is a leaf. - Bertran Steinsky, Mar 04 2014

a(n) = 2^(n-1) * A182166(n) for n>=2. - Joerg Arndt, Mar 12 2014

EXAMPLE

G.f. = 2*x^2 + 12*x^3 + 96*x^4 + 1280*x^5 + 30720*x^6 + 1376256*x^7 + ...

MAPLE

A095338:=n->n*(n-1)*2^binomial(n-1, 2): seq(A095338(n), n=1..20); # Wesley Ivan Hurt, Oct 17 2014

MATHEMATICA

Table[n (n - 1) 2^(Binomial[n-1, 2]), {n, 20}] (* Vincenzo Librandi, Mar 14 2014 *)

PROG

(PARI) a(n) = n*(n-1)*2^binomial(n-1, 2); \\ Joerg Arndt, Mar 12 2014

(MAGMA) [n*(n-1)*2^Binomial(n-1, 2): n in [1..20]]; // Vincenzo Librandi, Mar 14 2014

CROSSREFS

Cf. A182166.

Sequence in context: A052611 A340938 A059864 * A308820 A322717 A219538

Adjacent sequences:  A095335 A095336 A095337 * A095339 A095340 A095341

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein, Jun 02 2004

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 August 4 14:28 EDT 2021. Contains 346447 sequences. (Running on oeis4.)