login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A337716 Number of graphs, where vertices are labeled with positive integers summing to n, and where identically labeled vertices are indistinguishable and cannot be connected with an edge. 3

%I #18 Apr 28 2021 19:09:27

%S 1,1,2,4,8,16,35,77,179,440,1160,3264,9950,33206,121943,494011,

%T 2235399,11391306,65287199,422908306,3130775625,26490210964,

%U 255257056748,2825013955541,36147331371446,531237157370531,8965348473026888

%N Number of graphs, where vertices are labeled with positive integers summing to n, and where identically labeled vertices are indistinguishable and cannot be connected with an edge.

%H Andrew Howroyd, <a href="/A337716/b337716.txt">Table of n, a(n) for n = 0..50</a> (terms 0..30 from Max Alekseyev)

%o (PARI)

%o permcount(v) = {my(m=1, s=0, k=0, t); for(i=1, #v, t=v[i]; k=if(i>1&&t==v[i-1], k+1, 1); m*=t*k; s+=t); s!/m}

%o cross(u, v) = {sum(i=1, #u, sum(j=1, #v, gcd(u[i], v[j])))}

%o R(n,m,u)={if(n==0, 1, sum(k=if(m==1, n, 0), n\m, my(s=0); forpart(p=k, s+=self()(n-m*k, m-1, concat(u,Vec(p)))*2^cross(p,u)*permcount(p)); s/k!))}

%o a(n)={R(n,n,[])} \\ _Andrew Howroyd_, Sep 18 2020

%Y Cf. A337717.

%K nonn

%O 0,3

%A _Max Alekseyev_ following a suggestion from _Franklin T. Adams-Watters_, Sep 16 2020

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 1 16:12 EST 2024. Contains 370442 sequences. (Running on oeis4.)