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A131312 Number of labeled 3-arch graphs on n nodes. 1
0, 0, 1, 1, 10, 380, 34405, 5919536, 1709074584, 764754595200, 501266271119625, 461131039993333600, 575567346874153958896, 948234014731772610333856, 2015213091846867369590804125, 5418520468131267088808607104000, 18128426763624683428523183481856000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

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

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 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 attached 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: A200804 A277663 A000591 * A055733 A203774 A024136

Adjacent sequences:  A131309 A131310 A131311 * A131313 A131314 A131315

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

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Last modified September 22 17:16 EDT 2020. Contains 337291 sequences. (Running on oeis4.)