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A208408 T(n,k) is the number of n X k 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than two of its immediate leftward or upward or right-upward antidiagonal neighbors.

%I A208408 #12 Oct 15 2024 15:42:03
%S A208408 1,2,2,5,15,5,15,182,187,15,51,2698,10682,2795,51,187,41914,658450,
%T A208408 667478,43947,187,715,658450,40883360,163422914,42012698,700075,715,
%U A208408 2795,10370330,2540446156,40039156736,40595679634,2646531062,11188907,2795
%N A208408 T(n,k) is the number of n X k 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than two of its immediate leftward or upward or right-upward antidiagonal neighbors.
%H A208408 R. H. Hardin, <a href="/A208408/b208408.txt">Table of n, a(n) for n = 1..198</a>
%e A208408 Table starts:
%e A208408 ....1.........2..............5.................15......................51
%e A208408 ....2........15............182...............2698...................41914
%e A208408 ....5.......187..........10682.............658450................40883360
%e A208408 ...15......2795.........667478..........163422914.............40039156736
%e A208408 ...51.....43947.......42012698........40595679634..........39216100214432
%e A208408 ..187....700075.....2646531062.....10084768380770.......38410047476679936
%e A208408 ..715..11188907...166729574522...2505261257850802....37620564383817645696
%e A208408 .2795.178973355.10503950018198.622357842865595522.36847308431734650845696
%e A208408 ...
%e A208408 Some solutions for n=4 and k=3:
%e A208408 ..0..0..0....0..0..1....0..1..0....0..0..0....0..1..0....0..0..0....0..1..1
%e A208408 ..0..1..0....0..0..0....0..2..2....0..1..1....0..2..3....0..1..2....0..0..0
%e A208408 ..1..2..1....0..1..1....1..2..1....2..0..2....3..0..0....2..1..1....0..1..1
%e A208408 ..0..1..3....1..2..3....1..3..2....2..1..0....2..1..3....0..1..1....0..2..1
%Y A208408 Row 1 and column 1 are A007581(n-1).
%Y A208408 Columns 2..7 are A208402, A208403, A208404, A208405, A208406, A208407.
%Y A208408 Rows 2..7 are A208409, A208410, A208411, A208412, A208413, A208414.
%Y A208408 Main diagonal is A208401.
%K A208408 nonn,tabl
%O A208408 1,2
%A A208408 _R. H. Hardin_, Feb 26 2012