This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A184052 #18 Jun 02 2025 03:23:59 %S A184052 1,2,5,13,30,66,137,279,556,1104,2179,4309,8518,16886,33509,66643, %T A184052 132672,264492,527639,1053441,2104042,4204242,8402617,16797343, %U A184052 33582724,67149416,134274635,268516909,536985102,1073905134,2147712461,4295294379,8590392712,17180523876,34360655167,68720786713 %N A184052 The number of order-decreasing partial isometries (of an n-chain). %H A184052 R. Kehinde, S. O. Makanjuola and A. Umar, <a href="http://arxiv.org/abs/1101.2558">On the semigroup of order-decreasing partial isometries of a finite chain</a>, arXiv:1101.2558 %H A184052 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (5,-7,-3,16,-14,4). %F A184052 a(n) = 3*a(n-1)-2*a(n-2)-2^floor(n/2)+n+1. %F A184052 G.f.: ( -1+3*x-2*x^2-5*x^3-4*x^5+10*x^4 ) / ( (2*x-1)*(2*x^2-1)*(x-1)^3 ). - _R. J. Mathar_, Jul 03 2011 %e A184052 a(2) = 5 because there are exactly 5 order-decreasing partial isometries (on a 2-chain) namely: empty map; 1-->1; 2-->1; 2-->2; (1,2)-->(1,2) - the mappings are coordinate-wise %Y A184052 It is the row sum of A184051 %K A184052 nonn %O A184052 0,2 %A A184052 _Abdullahi Umar_, Jan 12 2011