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A200974 T(n,k) is the number of n X k 0..6 arrays with every row and column running average nondecreasing rightwards and downwards.

%I A200974 #9 Apr 27 2025 09:08:19
%S A200974 7,28,28,106,336,106,388,3636,3636,388,1387,37254,110854,37254,1387,
%T A200974 4874,368218,3167295,3167295,368218,4874,16919,3543465,86468392,
%U A200974 250149820,86468392,3543465,16919,58198,33420304,2279060645,18714498069
%N A200974 T(n,k) is the number of n X k 0..6 arrays with every row and column running average nondecreasing rightwards and downwards.
%H A200974 R. H. Hardin, <a href="/A200974/b200974.txt">Table of n, a(n) for n = 1..60</a>
%e A200974 Table starts:
%e A200974 ......7.........28...........106............388............1387............4874
%e A200974 .....28........336..........3636..........37254..........368218.........3543465
%e A200974 ....106.......3636........110854........3167295........86468392......2279060645
%e A200974 ....388......37254.......3167295......250149820.....18714498069...1342587653727
%e A200974 ...1387.....368218......86468392....18714498069...3807002935896.738228105542702
%e A200974 ...4874....3543465....2279060645..1342587653727.738228105542702
%e A200974 ..16919...33420304...58497330607.93360032845673
%e A200974 ..58198..310188575.1470248361721
%e A200974 .198807.2842734858
%e A200974 .675372
%e A200974 Some solutions for n=3 and k=3:
%e A200974 ..0..0..1....0..0..0....0..1..1....0..0..3....0..4..5....0..0..1....1..1..4
%e A200974 ..0..0..3....0..0..3....0..1..1....2..2..6....2..4..5....4..4..5....1..5..6
%e A200974 ..0..4..4....4..4..4....0..5..4....1..6..6....2..4..5....2..3..3....2..6..5
%Y A200974 Column 1 is A200762.
%K A200974 nonn,tabl
%O A200974 1,1
%A A200974 _R. H. Hardin_, Nov 25 2011