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A278319 Number of n X 2 0..1 arrays with rows and columns in lexicographic nondecreasing order but with exactly two mistakes.

%I A278319 #8 Feb 09 2019 09:33:16
%S A278319 0,3,20,94,395,1492,4991,14848,39832,97835,223015,477126,966849,
%T A278319 1869504,3470210,6214384,10780448,18178763,29884150,48010910,75541039,
%U A278319 116618372,176923705,264148560,388588200,563877795,807899313,1143890790,1601794149
%N A278319 Number of n X 2 0..1 arrays with rows and columns in lexicographic nondecreasing order but with exactly two mistakes.
%H A278319 R. H. Hardin, <a href="/A278319/b278319.txt">Table of n, a(n) for n = 1..210</a>
%F A278319 Empirical: a(n) = (1/39916800)*n^11 + (1/725760)*n^10 + (13/362880)*n^9 + (43/120960)*n^8 + (223/172800)*n^7 - (227/34560)*n^6 + (1019/45360)*n^5 + (27263/181440)*n^4 + (12193/113400)*n^3 - (121/840)*n^2 - (13/99)*n.
%F A278319 Conjectures from _Colin Barker_, Feb 09 2019: (Start)
%F A278319 G.f.: x^2*(3 - 16*x + 52*x^2 - 73*x^3 + 41*x^4 + x^5 - 10*x^6 + 3*x^7) / (1 - x)^12.
%F A278319 a(n) = 12*a(n-1) - 66*a(n-2) + 220*a(n-3) - 495*a(n-4) + 792*a(n-5) - 924*a(n-6) + 792*a(n-7) - 495*a(n-8) + 220*a(n-9) - 66*a(n-10) + 12*a(n-11) - a(n-12) for n>12.
%F A278319 (End)
%e A278319 Some solutions for n=4:
%e A278319 ..1..0. .0..1. .1..1. .1..0. .0..0. .1..1. .1..0. .1..1. .1..0. .1..0
%e A278319 ..1..0. .0..0. .0..1. .1..1. .1..1. .0..1. .0..0. .0..1. .0..0. .1..1
%e A278319 ..1..0. .1..0. .1..1. .0..1. .1..1. .0..0. .1..0. .0..0. .0..1. .1..1
%e A278319 ..0..0. .0..1. .0..1. .0..1. .1..0. .1..0. .1..0. .0..0. .1..1. .1..0
%Y A278319 Column 2 of A278325.
%K A278319 nonn
%O A278319 1,2
%A A278319 _R. H. Hardin_, Nov 18 2016