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A201072 T(n,k)=Number of nXk 0..6 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

%I A201072 #7 Jul 22 2025 16:04:49
%S A201072 7,21,21,35,70,35,35,35,35,35,21,77,514,77,21,7,749,2611,2611,749,7,1,
%T A201072 972,3937,22440,3937,972,1,7,127,50334,43308,43308,50334,127,7,21,
%U A201072 3034,4448,1127514,2250982,1127514,4448,3034,21,35,7161,381982,175865
%N A201072 T(n,k)=Number of nXk 0..6 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.
%C A201072 Table starts
%C A201072 ..7...21......35........35.........21.............7.............1
%C A201072 .21...70......35........77........749...........972...........127
%C A201072 .35...35.....514......2611.......3937.........50334..........4448
%C A201072 .35...77....2611.....22440......43308.......1127514........175865
%C A201072 .21..749....3937.....43308....2250982......11512566.......3558888
%C A201072 ..7..972...50334...1127514...11512566......45244488......76714325
%C A201072 ..1..127....4448....175865....3558888......76714325....1001060834
%C A201072 ..7.3034..381982..20393189..473983329....4070916182...13053459189
%C A201072 .21.7161..206357..14766300.4102010820...93433967419..126679336122
%C A201072 .35.2170.1377351.158314010.3773723044.1001816580924.1146503112430
%H A201072 R. H. Hardin, <a href="/A201072/b201072.txt">Table of n, a(n) for n = 1..143</a>
%F A201072 T(n,1) = binomial(7,n modulo 7). For a 0..z array, T(n,1) = binomial(z+1, n modulo (z+1)).
%e A201072 Some solutions for n=3 k=7
%e A201072 ..0..0..1..1..3..4..5....0..0..1..1..3..4..4....0..0..1..1..2..4..4
%e A201072 ..0..2..2..3..4..5..6....0..2..2..3..3..5..6....0..1..3..3..4..5..5
%e A201072 ..1..2..3..4..5..6..6....1..2..4..5..5..6..6....2..2..3..5..6..6..6
%K A201072 nonn,tabl
%O A201072 1,1
%A A201072 _R. H. Hardin_ Nov 26 2011