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A200858 T(n,k)=Number of nXk 0..4 arrays with every row and column running average nondecreasing rightwards and downwards.

%I A200858 #7 Jul 22 2025 15:59:08
%S A200858 5,15,15,42,105,42,113,647,647,113,297,3728,8535,3728,297,767,20656,
%T A200858 103528,103528,20656,767,1957,111222,1194898,2604826,1194898,111222,
%U A200858 1957,4947,586908,13295014,61846403,61846403,13295014,586908,4947,12419
%N A200858 T(n,k)=Number of nXk 0..4 arrays with every row and column running average nondecreasing rightwards and downwards.
%C A200858 Table starts
%C A200858 .....5.......15...........42............113.............297..............767
%C A200858 ....15......105..........647...........3728...........20656...........111222
%C A200858 ....42......647.........8535.........103528.........1194898.........13295014
%C A200858 ...113.....3728.......103528........2604826........61846403.......1408572430
%C A200858 ...297....20656......1194898.......61846403......3001883019.....139139776965
%C A200858 ...767...111222.....13295014.....1408572430....139139776965...13079416454738
%C A200858 ..1957...586908....144195756....31197299012...6255225014290.1191594088382132
%C A200858 ..4947..3047226...1532754468...676213941385.274516401002582
%C A200858 .12419.15620118..16036647028.14409889137860
%C A200858 .31006.79228317.165590166035
%H A200858 R. H. Hardin, <a href="/A200858/b200858.txt">Table of n, a(n) for n = 1..84</a>
%e A200858 Some solutions for n=5 k=3
%e A200858 ..0..0..0....0..0..0....0..0..0....0..0..1....0..0..0....0..0..0....0..0..0
%e A200858 ..0..0..2....0..0..2....0..0..0....0..0..1....0..0..0....0..0..2....0..0..0
%e A200858 ..0..0..2....0..1..3....0..3..2....0..2..2....0..0..2....0..3..4....0..3..4
%e A200858 ..0..2..4....0..3..2....0..1..4....0..3..3....0..4..4....0..4..4....0..3..4
%e A200858 ..3..3..4....0..2..2....3..3..4....0..2..2....0..4..4....0..2..3....1..2..4
%Y A200858 Column 1 is A200760
%K A200858 nonn,tabl
%O A200858 1,1
%A A200858 _R. H. Hardin_ Nov 23 2011