cp's OEIS Frontend

A127912 Number of nonisomorphic disconnected mappings (or mapping patterns) from n points to themselves; number of disconnected endofunctions.

%I A127912 #14 Feb 16 2025 08:33:04
%S A127912 0,1,3,10,27,79,218,622,1753,5007,14274,40954,117548,338485,975721,
%T A127912 2817871,8146510,23581381,68322672,198138512,575058726,1670250623,
%U A127912 4854444560,14117859226,41081418963,119606139728
%N A127912 Number of nonisomorphic disconnected mappings (or mapping patterns) from n points to themselves; number of disconnected endofunctions.
%C A127912 Number of endofunctions on n points whose functional digraphs (with loops allowed) are nontrivially the directed sum of two or more digraphs of endofunctions.
%D A127912 Steven R. Finch, Mathematical Constants, Cambridge, 2003, Section 5.6.6.
%D A127912 R. A. Fisher, Contributions to Mathematical Statistics, Wiley, 1950, 41.399 and 41.401.
%H A127912 N. G. de Bruijn and D. A. Klarner, <a href="https://pure.tue.nl/ws/files/1674487/597568.pdf">Multisets of aperiodic cycles</a>, SIAM J. Algebraic Discrete Methods 3 (1982), no. 3, 359--368. MR0666861(84i:05008).
%H A127912 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FunctionalGraph.html">Functional Graph.</a>
%F A127912 a(n) = A001372(n) - A002861(n).
%e A127912 a(0) = 0, as the null digraph is formally neither connected nor disconnected.
%e A127912 a(1) = 0, as the unique endofunction on one point is the identity function on one value and is connected.
%e A127912 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.
%e A127912 a(3) = A001372(3) - A002861(3) = 7 - 4 = 3.
%e A127912 a(4) = A001372(4) - A002861(4) = 19 - 9 = 10.
%e A127912 a(5) = A001372(5) - A002861(5) = 47 - 20 = 27.
%e A127912 a(6) = 130 - 51 = 79.
%e A127912 a(7) = 343 - 125 = 218.
%e A127912 a(8) = 951 - 329 = 622.
%e A127912 a(9) = 2615 - 862 = 1753.
%e A127912 a(10) = 7318 - 2311 = 5007.
%Y A127912 Cf. A000081, A000273, A001372, A002861, A003027, A003085, A062738, A116950, A126285, A127909-A127915.
%K A127912 easy,nonn
%O A127912 0,3
%A A127912 _Jonathan Vos Post_, Feb 06 2007