%I #4 Nov 22 2016 06:56:13

%S 0,6,6,40,100,40,155,1609,1609,155,456,19624,57760,19624,456,1128,

%T 178352,2116789,2116789,178352,1128,2472,1287838,67971132,223202074,

%U 67971132,1287838,2472,4950,7795151,1796061464,23450120081,23450120081,1796061464

%N T(n,k)=Number of nXk 0..3 arrays with rows and columns in lexicographic nondecreasing order but with exactly one mistake.

%C Table starts

%C ....0.......6.........40...........155..............456................1128

%C ....6.....100.......1609.........19624...........178352.............1287838

%C ...40....1609......57760.......2116789.........67971132..........1796061464

%C ..155...19624....2116789.....223202074......23450120081.......2266913897519

%C ..456..178352...67971132...23450120081....7817299555828....2573951428892959

%C .1128.1287838.1796061464.2266913897519.2573951428892959.2817080307689646420

%H R. H. Hardin, <a href="/A278435/b278435.txt">Table of n, a(n) for n = 1..97</a>

%F Empirical for column k:

%F k=1: [polynomial of degree 7]

%F k=2: [polynomial of degree 31]

%F k=3: [polynomial of degree 127]

%e Some solutions for n=3 k=4

%e ..0..0..0..3. .0..0..2..0. .0..0..2..2. .0..0..1..3. .0..0..0..1

%e ..1..1..3..0. .0..1..0..0. .0..2..3..0. .1..3..2..1. .1..1..3..0

%e ..0..3..3..0. .0..1..3..2. .0..3..2..1. .0..3..0..1. .0..2..2..2

%Y Column 1 is A001919(n+1).

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Nov 22 2016