A131313 - OEIS

%I #15 Feb 16 2024 21:07:13

%S 0,0,0,1,1,15,1085,216230,92550276,74358276300,102660061574400,

%T 228311514581611725,777903709095959606875,3900045557544532389044051,

%U 27829438251904221299882526375,274842860343937013061411903607000,3668195394384971166861021308091920000

%N Number of labeled 4-arch graphs on n nodes.

%H Allan Bickle,  <a href="https://digitalcommons.georgiasouthern.edu/cgi/viewcontent.cgi?article=1409&amp;context=tag">A Survey of Maximal k-degenerate Graphs and k-Trees</a>, Theory and Applications of Graphs 0 1 (2024) Article 5.

%H Saverio Caminiti and Emanuele G. Fusco, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL10/Caminiti/caminiti.html">On the Number of Labeled k-arch Graphs</a>, Journal of Integer Sequences, Vol 10 (2007), Article 07.7.5

%F The number of labeled 4-arch graphs with n>5 nodes is given by f(n,4,n-4-1,0,4) where f is the recursive function described by the PARI/GP code below.

%o (PARI) f(n,k,i,u,j)={ local(s=0); if (i==1, binomial(n-u,j)*binomial(u,k-j), for (c=0, min(k,n-(i-1)-(u+j)), s+=f(n,k,i-1,u+j,c) ); binomial(n-u,j)*binomial(u,k-j)*s ) }

%Y Cf. A098721-A098724, A131311-A131315.

%K nonn

%O 1,6

%A Saverio Caminiti and Emanuele G. Fusco (fusco(AT)di.uniroma1.it), Sep 18 2007

%E Edited by _N. J. A. Sloane_, Oct 02 2007

%E Terms a(11) and beyond from _Andrew Howroyd_, Nov 07 2019