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%I #16 Apr 16 2023 12:33:18
%S 1,2,5,13,30,66,137,279,556,1104,2179,4309,8518,16886,33509,66643,
%T 132672,264492,527639,1053441,2104042,4204242,8402617,16797343,
%U 33582724,67149416,134274635,268516909,536985102,1073905134,2147712461,4295294379,8590392712,17180523876,34360655167,68720786713
%N The number of order-decreasing partial isometries (of an n-chain)
%H 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 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (5,-7,-3,16,-14,4).
%F a(n) = 3*a(n-1)-2*a(n-2)-2^floor(n/2)+n+1.
%F 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 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 It is the row sum of A184051
%K nonn
%O 0,2
%A _Abdullahi Umar_, Jan 12 2011