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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. 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 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

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