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A005646 Number of classifications of n elements.
(Formerly M2600)
1, 1, 1, 3, 6, 26, 122, 1015, 11847, 208914, 5236991, 184321511 (list; graph; refs; listen; history; text; internal format)



"A 'classification' is a set of n type-specimens each one of which is corralled on its own by the union of a set of binary partitions, none of which could be omitted without leaving 2 types unseparated".

From Robert Munafo, Jan 24 2010: (Start)

Extensive explanation with illustrations on Munafo web page.

This sequence gives the row sums of triangle A171871. (End)


N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

P. J. Wexler, On the number of taxonomies; or the odds on 'structuralism', American Anthropologist, 73 (1971), 1258.


Table of n, a(n) for n=1..12.

Robert Munafo, Web page about this sequence (with additional terms) [Added Jan 04 2010]

P. J. Wexler and D. H. Fremlin, The number of classifications of up to seven classificanda, Classification Society Bull., 4 (No. 3, 1979), 2-4. (Annotated scanned copy)


Illustrated examples on Munafo web page. - Robert Munafo, Jan 24 2010


Cf. A000055, A171872, A171873. - Robert Munafo, Jan 24 2010

Sequence in context: A058258 A215397 A214309 * A033194 A304051 A128437

Adjacent sequences:  A005643 A005644 A005645 * A005647 A005648 A005649




N. J. A. Sloane


1015 term first calculated by Andrew Weimholt, Dec 15 2009

11847 term first calculated by Andrew Weimholt, Dec 19 2009

208914 term first calculated by Robert Munafo, Dec 29 2009

5236990 term (erroneous) from Robert Munafo, Dec 30 2009

Erroneous "5236990" corrected to 5236991 by Robert Munafo, Jan 01 2010

184321511 term first calculated by Robert Munafo, Jan 10 2010



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Last modified October 3 22:17 EDT 2022. Contains 357237 sequences. (Running on oeis4.)