%I
%S 0,0,4,65,456,2128,7728,23607,63460,154518,347568,732524,1461824,
%T 2784600,5095376,9002010,15418728,25691420,41763900,66395595,
%U 103443144,158220680,237956160,352364025,514357740,740929410,1054227720,1482869934
%N Number of n X 1 0..3 arrays with rows and columns in lexicographic nondecreasing order but with exactly two mistakes.
%C Column 1 of A278553.
%H R. H. Hardin, <a href="/A278547/b278547.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/39916800)*n^11 + (1/604800)*n^10 + (1/20736)*n^9 + (5/8064)*n^8 + (553/172800)*n^7  (97/28800)*n^6  (25591/725760)*n^5 + (89/24192)*n^4 + (13607/129600)*n^3  (47/50400)*n^2  (289/3960)*n.
%F Empirical g.f.: x^3*(4 + 17*x  60*x^2 + 66*x^3  32*x^4 + 6*x^5) / (1  x)^12.  _Colin Barker_, Mar 22 2018
%e Some solutions for n=4:
%e ..3. .0. .2. .2. .2. .3. .3. .1. .2. .2. .2. .3. .3. .2. .3. .2
%e ..1. .2. .0. .1. .1. .2. .1. .0. .1. .1. .0. .2. .0. .0. .1. .3
%e ..1. .1. .3. .2. .3. .0. .3. .2. .0. .0. .2. .0. .3. .3. .0. .2
%e ..0. .0. .1. .0. .1. .1. .2. .0. .1. .3. .0. .2. .2. .2. .2. .0
%Y Cf. A278553.
%K nonn
%O 1,3
%A _R. H. Hardin_, Nov 23 2016
