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T(n,k) = Number of n X k arrays containing k copies of 0..n-1 with no element plus any horizontal or antidiagonal neighbor equal to n-1.
5

%I #8 Apr 20 2021 12:29:39

%S 1,0,2,0,0,6,0,0,10,24,0,0,30,248,120,0,0,42,3344,14928,720,0,0,154,

%T 74416,2450392,829824,5040,0,0,478,1738864,589295880,1627602144,

%U 90999072,40320,0,0,2086,50328912,161738440488,4883292435072,2887429166352

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

%C Table starts

%C .......1.............0................0..................0.................0

%C .......2.............0................0..................0.................0

%C .......6............10...............30.................42...............154

%C ......24...........248.............3344..............74416...........1738864

%C .....120.........14928..........2450392..........589295880......161738440488

%C .....720........829824.......1627602144......4883292435072.17590000594071456

%C ....5040......90999072....2887429166352.137248106312324496

%C ...40320....9589855104.4949478766305024

%C ..362880.1679970554880

%C .3628800

%H R. H. Hardin, <a href="/A265856/b265856.txt">Table of n, a(n) for n = 1..60</a>

%e Some solutions for n=4, k=4

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

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

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

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

%Y Column 1 is A000142.

%K nonn,tabl

%O 1,3

%A _R. H. Hardin_, Dec 16 2015