login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A127912 Number of nonisomorphic disconnected mappings (or mapping patterns) from n points to themselves; number of disconnected endofunctions. 0
0, 1, 3, 10, 27, 79, 218, 622, 1753, 5007, 14274, 40954, 117548, 338485, 975721, 2817871, 8146510, 23581381, 68322672, 198138512, 575058726, 1670250623, 4854444560, 14117859226, 41081418963, 119606139728 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Number of endofunctions on n points whose functional digraphs (with loops allowed) are nontrivially the directed sum of two or more digraphs of endofunctions.

REFERENCES

S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 5.6.6.

R. A. Fisher, Contributions to Mathematical Statistics, Wiley, 1950, 41.399 and 41.401.

N. G. de Bruijn and D. A. Klarner, Multisets of aperiodic cycles, SIAM J, Algeb. Discrete Meth., 3 (1982), 359-368.

LINKS

Table of n, a(n) for n=0..25.

Eric Weisstein's World of Mathematics, Functional Graph.

FORMULA

a(n) = A001372(n) - A002861(n).

EXAMPLE

a(0) = 0, as the null digraph is formally neither connected nor disconnected.

a(1) = 0, as the unique endofunction on one point is the identity function on one value and is connected.

a(2) = 1, as there are 3 endofunctions on two points, two of which are "prime endofunctions" and one of which is the direct sum of two copies of the unique endofunction on one point, namely two points-with-loops, or the identity function on two values; 3 - 2 = 1.

a(3) = A001372(3) - A002861(3) = 7 - 4 = 3.

a(4) = A001372(4) - A002861(4) = 19 - 9 = 10.

a(5) = A001372(5) - A002861(5) = 47 - 20 = 27.

a(6) = 130 - 51 = 79.

a(7) = 343 - 125 = 218.

a(8) = 951 - 329 = 622.

a(9) = 2615 - 862 = 1753.

a(10) = 7318 - 2311 = 5007.

CROSSREFS

Cf. A000081, A000273, A001372, A002861, A003027, A003085, A062738, A116950, A126285, A127909-A127915.

Sequence in context: A154496 A027251 A279136 * A005956 A262724 A059193

Adjacent sequences:  A127909 A127910 A127911 * A127913 A127914 A127915

KEYWORD

easy,nonn,changed

AUTHOR

Jonathan Vos Post, Feb 06 2007

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified November 18 12:21 EST 2017. Contains 294891 sequences.