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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A144208 Number of simple graphs on n labeled nodes, where each maximally connected subgraph consists of a single node or has a unique cycle of length 3; also row sums of A144207. 3
1, 1, 1, 2, 17, 221, 3261, 54801, 1049235, 22695027, 548904831, 14701691121, 432342705351, 13856514927207, 480891887472585, 17971038945463101, 719613541474095591, 30743125693699501431, 1395902175504288127695 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..150

FORMULA

a(n) = Sum_{k=0..n} A144207(n,k).

a(n) ~ c * n^(n-1), where c = 0.762590842281789937101466... . - Vaclav Kotesovec, Sep 10 2014

EXAMPLE

a(3) = 2, because there are 2 simple graphs on 3 labeled nodes, where each maximally connected subgraph consists of a single node or has a unique cycle of length 3:

.1.2. .1-2.

..... .|/..

.3... .3...

MAPLE

T:= proc(n, k) option remember; if k=0 then 1 elif k<0 or n<k then 0 elif k=n then binomial(n-1, 2) *n^(n-3) else T(n-1, k) +add(binomial(n-1, j) * T(j+1, j+1) *T(n-1-j, k-j-1), j=2..k-1) fi end: a:= n-> add(T(n, k), k=0..n): seq(a(n), n=0..23);

MATHEMATICA

T[n_, k_] := T[n, k] = Which[k == 0, 1, k<0 || n<k, 0, k == n, Binomial[n-1, 2] *n^(n-3), True, T[n-1, k] + Sum[Binomial[n-1, j] * T[j+1, j+1] * T[n-1-j, k-j-1], {j, 2, k-1}]]; a[n_] := Sum[T[n, k], {k, 0, n}]; Table[a[n], {n, 0, 23}] (* Jean-Fran├žois Alcover, Feb 05 2015, after Alois P. Heinz *)

CROSSREFS

Row sums of triangle A144207. A column of A144212. Cf. A053507, A007318.

Sequence in context: A277768 A004029 A114268 * A183711 A058239 A006227

Adjacent sequences:  A144205 A144206 A144207 * A144209 A144210 A144211

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 14 2008

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 September 18 10:30 EDT 2019. Contains 327170 sequences. (Running on oeis4.)