%I #9 Mar 22 2018 09:46:49
%S 0,0,0,0,6,77,504,2304,8350,25653,69576,171106,388752,827190,1665456,
%T 3198312,5895396,10483934,18062160,30252180,49402850,78855339,
%U 123286440,189147400,285219090,423307755,619109400,893275110,1272714300,1792178076
%N Number of n X 1 0..2 arrays with rows and columns in lexicographic nondecreasing order but with exactly three mistakes.
%C Column 1 of A278372.
%H R. H. Hardin, <a href="/A278365/b278365.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/39916800)*n^11 + (1/604800)*n^10 + (17/725760)*n^9 - (1/10080)*n^8 - (227/172800)*n^7 + (193/28800)*n^6 - (1273/725760)*n^5 - (1909/60480)*n^4 + (31169/907200)*n^3 + (629/25200)*n^2 - (31/990)*n.
%F Empirical g.f.: x^5*(2 - x)*(3 - 2*x)*(1 + 2*x - 2*x^2) / (1 - x)^12. - _Colin Barker_, Mar 22 2018
%e Some solutions for n=8:
%e ..0. .2. .2. .1. .1. .0. .2. .2. .2. .2. .2. .0. .2. .2. .2. .2
%e ..2. .0. .2. .0. .2. .2. .0. .0. .0. .0. .2. .1. .2. .0. .1. .0
%e ..1. .0. .2. .2. .1. .1. .1. .1. .2. .1. .2. .0. .1. .0. .0. .2
%e ..2. .1. .1. .0. .0. .0. .2. .0. .0. .0. .1. .2. .2. .1. .1. .2
%e ..0. .0. .0. .2. .2. .2. .0. .1. .1. .1. .0. .0. .0. .0. .2. .1
%e ..0. .2. .2. .1. .0. .0. .1. .1. .0. .2. .1. .2. .2. .1. .2. .1
%e ..2. .1. .0. .2. .2. .0. .0. .0. .0. .2. .1. .1. .1. .1. .0. .0
%e ..0. .1. .2. .2. .2. .1. .1. .1. .2. .0. .0. .2. .2. .0. .0. .2
%Y Cf. A278372.
%K nonn
%O 1,5
%A _R. H. Hardin_, Nov 19 2016