login
T(n,k)=Number of nXk arrays containing k copies of 0..n-1 with no element plus any antidiagonal neighbor equal to n-1.
7

%I #6 Aug 12 2016 06:55:34

%S 1,1,2,1,2,6,1,4,42,24,1,6,340,984,120,1,12,3136,56496,48216,720,1,20,

%T 30456,3965392,28645840,2869200,5040,1,40,307464,307543008,

%U 21193260208,20091622560,278125200,40320,1,70,3182784,25346247472,17674408924672

%N T(n,k)=Number of nXk arrays containing k copies of 0..n-1 with no element plus any antidiagonal neighbor equal to n-1.

%C Table starts

%C ......1.............1.................1...................1...................1

%C ......2.............2.................4...................6..................12

%C ......6............42...............340................3136...............30456

%C .....24...........984.............56496.............3965392...........307543008

%C ....120.........48216..........28645840.........21193260208......17674408924672

%C ....720.......2869200.......20091622560.....187225073253120.2036853990307247808

%C ...5040.....278125200....29056095714720.4173639524545757568

%C ..40320...31015797120.52981034285587200

%C .362880.4991834736000

%H R. H. Hardin, <a href="/A265870/b265870.txt">Table of n, a(n) for n = 1..60</a>

%e Some solutions for n=3 k=4

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

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

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

%Y Column 1 is A000142.

%Y Row 2 is A063886.

%K nonn,tabl

%O 1,3

%A _R. H. Hardin_, Dec 17 2015