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A005646 Classifications of n elements.
(Formerly M2600)
9
1, 1, 1, 3, 6, 26, 122, 1015, 11847, 208914, 5236991, 184321511 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

"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)

REFERENCES

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.

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

LINKS

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

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

EXAMPLE

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

CROSSREFS

Cf. A000055, A171872, A171873. [From Robert Munafo, Jan 24 2010]

Sequence in context: A058258 A215397 A214309 * A033194 A128437 A200654

Adjacent sequences:  A005643 A005644 A005645 * A005647 A005648 A005649

KEYWORD

nonn,nice,more

AUTHOR

N. J. A. Sloane.

EXTENSIONS

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

STATUS

approved

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Last modified July 21 08:24 EDT 2017. Contains 289637 sequences.