# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a131520 Showing 1-1 of 1 %I A131520 #41 Jul 18 2022 20:42:12 %S A131520 2,6,12,22,40,74,140,270,528,1042,2068,4118,8216,16410,32796,65566, %T A131520 131104,262178,524324,1048614,2097192,4194346,8388652,16777262, %U A131520 33554480,67108914,134217780,268435510,536870968,1073741882,2147483708 %N A131520 Number of partitions of the graph G_n (defined below) into "strokes". %C A131520 G_n = {V_n, E_n}, V_n = {v_1, v_2, ..., v_n}, E_n = {v_1 v_2, v_2 v_3, ..., v_{n-1} v_n, v_n v_1} %C A131520 See the definition of "stroke" in A089243. %C A131520 A partition of a graph G into strokes S_i must satisfy the following conditions, where H is a digraph on G: %C A131520 - Union_{i} S_i = H, %C A131520 - i != j => S_i and S_j do not have a common edge, %C A131520 - i != j => S_i U S_j is not a directed path, %C A131520 - For all i, S_i is a dipath. %C A131520 a(n) is also the number of maximal subsemigroups of the monoid of partial order preserving mappings on a set with n elements. - _James Mitchell_ and _Wilf A. Wilson_, Jul 21 2017 %H A131520 G. C. Greubel, Table of n, a(n) for n = 1..1000 %H A131520 James East, Jitender Kumar, James D. Mitchell, and Wilf A. Wilson, Maximal subsemigroups of finite transformation and partition monoids, arXiv:1706.04967 [math.GR], 2017. [_James Mitchell_ and _Wilf A. Wilson_, Jul 21 2017] %H A131520 Index entries for linear recurrences with constant coefficients, signature (4,-5,2). %F A131520 a(n) = 2*(n-1) + 2^n = 2*A006127(n-1). %F A131520 G.f.: 2*x*(1 - x - x^2)/((1-x)^2 * (1-2*x)). - _R. J. Mathar_, Nov 14 2007 %F A131520 a(n) = 4*a(n-1)-5*a(n-2)+2*a(n-3). - _Wesley Ivan Hurt_, May 20 2021 %e A131520 Figure for G_4: o-o-o-o-o Two vertices on both sides are the same. %t A131520 Table[2^n + 2*(n-1), {n, 30}] (* _G. C. Greubel_, Feb 13 2021 *) %o A131520 (Sage) [2^n + 2*(n-1) for n in (1..30)] # _G. C. Greubel_, Feb 13 2021 %o A131520 (Magma) [2^n + 2*(n-1): n in [1..30]]; // _G. C. Greubel_, Feb 13 2021 %Y A131520 Cf. A131518, A173740, A354228. %K A131520 nonn,easy %O A131520 1,1 %A A131520 _Yasutoshi Kohmoto_, Aug 15 2007 %E A131520 More terms from _Max Alekseyev_, Sep 29 2007 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE