A195912 Number of proper (n,3)-clusterings.

1, 38, 675, 7840, 74291, 630546, 5014843, 38290580, 284670771, 2078666854, 14991726971, 107192696520, 761785678291, 5390429149562, 38025671502459, 267655258816060, 1881013969942451, 13204432684440270

Offset

3,2

Comments

See Roman et al. for precise definition.

Links

Table of n, a(n) for n=3..20.

Adam Roman, Igor T. Podolak and Agnieszka Deszynska, On the number of clusterings in a hierarchical classification model with overlapping clusters, Schedae Informaticae, Volume 20, 2011.

Formula

Roman et al. give an explicit formula.

Prog

(PARI) a(n) = {if (n==3, return (1)); n --; return (7*a(n) + 2*5^n - 3*4^n + (4*n-11)*3^n/6 + (4 - 15*n/4)*2^n + 9*n - 1/2); } \\ Michel Marcus, Apr 21 2013

Crossrefs

Sequence in context: A094034 A020931 A089271 * A240425 A269010 A010954

Adjacent sequences: A195909 A195910 A195911 * A195913 A195914 A195915

Keyword

nonn

Author

N. J. A. Sloane, May 06 2012

Extensions

More terms from Michel Marcus, Apr 21 2013

Status

approved