%I #15 Feb 16 2024 21:06:49
%S 0,0,1,1,10,380,34405,5919536,1709074584,764754595200,501266271119625,
%T 461131039993333600,575567346874153958896,948234014731772610333856,
%U 2015213091846867369590804125,5418520468131267088808607104000,18128426763624683428523183481856000
%N Number of labeled 3-arch graphs on n nodes.
%H Allan Bickle, <a href="https://digitalcommons.georgiasouthern.edu/cgi/viewcontent.cgi?article=1409&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 3-arch graphs with n>4 nodes is given by f(n,3,n-3-1,0,3) 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 1,5
%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
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