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%I #7 Feb 09 2019 14:35:57
%S 1,6,27,96,281,708,1590,3264,6237,11242,19305,31824,50661,78248,
%T 117708,172992,249033,351918,489079,669504,903969,1205292,1588610,
%U 2071680,2675205,3423186,4343301,5467312,6831501,8477136,10450968,12805760
%N Number of n X 2 0..1 arrays with rows and columns in lexicographic nondecreasing order but with exactly one mistake.
%H R. H. Hardin, <a href="/A278357/b278357.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/5040)*n^7 + (1/240)*n^6 + (31/720)*n^5 + (1/16)*n^4 + (41/360)*n^3 + (13/30)*n^2 + (12/35)*n.
%F Conjectures from _Colin Barker_, Feb 09 2019: (Start)
%F G.f.: x*(1 - 2*x + 7*x^2 - 8*x^3 + 3*x^4) / (1 - x)^8.
%F a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.
%F (End)
%e Some solutions for n=4:
%e ..1..1. .0..0. .0..0. .0..0. .0..1. .1..1. .1..1. .1..1. .1..1. .0..1
%e ..1..1. .1..1. .1..0. .1..0. .1..1. .1..1. .0..0. .0..1. .0..0. .1..1
%e ..1..1. .0..1. .1..0. .1..0. .0..1. .0..0. .0..0. .1..0. .0..1. .1..0
%e ..0..1. .0..1. .1..0. .1..1. .1..0. .0..0. .0..0. .1..0. .1..1. .1..1
%Y Column 2 of A278363.
%K nonn
%O 1,2
%A _R. H. Hardin_, Nov 19 2016
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