%I #6 May 28 2021 13:23:14

%S 754,8151,5125,90512,52962,35674,1012633,566649,418853,258746,

%T 11398109,6175841,5247300,3590945,1877439,128428125,68396118,67554413,

%U 54457598,31484714,13648650,1448958659,754814607,904486202,899378367,606913688

%N T(n,k) = Number of (n+2) X (k+2) 0..3 arrays with every consecutive three elements in every row having 2 or 3 distinct values, in every column 1 or 2 distinct values, in every diagonal 2 distinct values, and in every antidiagonal 2 distinct values, and new values 0 upwards introduced in row major order.

%C Table starts

%C ........754........8151.......90512......1012633.....11398109....128428125

%C .......5125.......52962......566649......6175841.....68396118....754814607

%C ......35674......418853.....5247300.....67554413....904486202..12006682353

%C .....258746.....3590945....54457598....899378367..16084394412.280079543014

%C ....1877439....31484714...606913688..13412317102.332404559794

%C ...13648650...273765237..6778023822.202527530051

%C ...99324229..2405660944.76682086492

%C ..722975673.21164695786

%C .5263920930

%H R. H. Hardin, <a href="/A252917/b252917.txt">Table of n, a(n) for n = 1..49</a>

%F Empirical for column k:

%F k=1: [linear recurrence of order 64] for n > 65.

%F Empirical for row n:

%F n=1: [linear recurrence of order 40] for n > 41.

%e Some solutions for n=2, k=4

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Dec 24 2014