1,7

Saverio Caminiti and Emanuele G. Fusco, On the Number of Labeled k-arch Graphs, Journal of Integer Sequences, Vol 10 (2007), Article 07.7.5

The number of labeled 5-arch graps with n>6 nodes is given by f(n,5,n-5-1,0,5) where f is the recursive function described by the pari-gp code attached below.

(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 ) }

Cf. A098721-A098724, A131311-A131315.

Sequence in context: A033510 A123844 A068254 this_sequence A122801 A099680 A114934

Adjacent sequences: A131311 A131312 A131313 this_sequence A131315 A131316 A131317

nonn

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

Edited by njas, Oct 02 2007