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Number of n X 2 0..1 arrays with rows in nondecreasing lexicographic order and columns in nonincreasing lexicographic order, but with exactly one mistake.
1

%I #8 Feb 10 2019 07:00:45

%S 1,8,33,99,245,532,1050,1926,3333,5500,8723,13377,19929,28952,41140,

%T 57324,78489,105792,140581,184415,239085,306636,389390,489970,611325,

%U 756756,929943,1134973,1376369,1659120,1988712,2371160,2813041,3321528

%N Number of n X 2 0..1 arrays with rows in nondecreasing lexicographic order and columns in nonincreasing lexicographic order, but with exactly one mistake.

%H R. H. Hardin, <a href="/A278670/b278670.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/720)*n^6 + (1/48)*n^5 + (23/144)*n^4 + (19/48)*n^3 + (61/180)*n^2 + (1/12)*n.

%F Conjectures from _Colin Barker_, Feb 10 2019: (Start)

%F G.f.: x*(1 + x - 2*x^2 + x^3) / (1 - x)^7.

%F a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

%F (End)

%e Some solutions for n=4:

%e ..1..0. .0..0. .1..0. .1..0. .0..1. .0..0. .0..0. .0..0. .0..0. .0..0

%e ..1..1. .1..0. .0..0. .1..1. .1..0. .0..0. .1..0. .1..0. .1..0. .0..0

%e ..0..0. .0..0. .0..0. .1..0. .1..1. .1..1. .0..1. .0..1. .0..0. .0..1

%e ..0..0. .1..1. .0..1. .1..0. .1..1. .1..0. .1..0. .0..1. .0..1. .1..0

%Y Column 2 of A278676.

%K nonn

%O 1,2

%A _R. H. Hardin_, Nov 25 2016