A131313 - OEIS

A131313

Number of labeled 4-arch graphs on n nodes.

0, 0, 0, 1, 1, 15, 1085, 216230, 92550276, 74358276300, 102660061574400, 228311514581611725, 777903709095959606875, 3900045557544532389044051, 27829438251904221299882526375, 274842860343937013061411903607000, 3668195394384971166861021308091920000

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OFFSET

1,6

LINKS

Table of n, a(n) for n=1..17.

Allan Bickle, A Survey of Maximal k-degenerate Graphs and k-Trees, Theory and Applications of Graphs 0 1 (2024) Article 5.

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

FORMULA

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.

PROG

(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 ) }

CROSSREFS

Cf. A098721-A098724, A131311-A131315.

Sequence in context: A206162 A203409 A207980 * A208346 A236329 A129764

Adjacent sequences: A131310 A131311 A131312 * A131314 A131315 A131316

KEYWORD

nonn

AUTHOR

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

EXTENSIONS

Edited by N. J. A. Sloane, Oct 02 2007

Terms a(11) and beyond from Andrew Howroyd, Nov 07 2019

STATUS

approved