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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. A002861 Number of connected functions (or mapping patterns) on n unlabeled points, or number of rings and branches with n edges. A001372 Number of mappings (or mapping patterns) from n points to themselves; number of endofunctions. a(n) is prime for n = 2, 6, 9, 18.

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). a(n) = (Euler transform of A002861) - (CIK transform of A000081).

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

AUTHOR

Jonathan Vos Post, Feb 06 2007

STATUS

approved

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Last modified September 22 09:19 EDT 2017. Contains 292336 sequences.