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A201451 T(n,k)=Number of nXk 0..3 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

%I A201451 #7 Jul 22 2025 16:15:47
%S A201451 4,6,6,4,2,4,1,21,21,1,4,9,52,9,4,6,56,29,29,56,6,4,13,246,112,246,13,
%T A201451 4,1,110,701,261,261,701,110,1,4,32,844,846,4544,846,844,32,4,6,198,
%U A201451 426,1720,22324,22324,1720,426,198,6,4,41,2478,4193,45532,16334,45532,4193
%N A201451 T(n,k)=Number of nXk 0..3 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.
%C A201451 Table starts
%C A201451 .4...6....4.....1.......4.......6........4........1..........4..........6
%C A201451 .6...2...21.....9......56......13......110.......32........198.........41
%C A201451 .4..21...52....29.....246.....701......844......426.......2478.......5990
%C A201451 .1...9...29...112.....261.....846.....1720.....4193.......8065......16693
%C A201451 .4..56..246...261....4544...22324....45532....32314.....313710....1126721
%C A201451 .6..13..701...846...22324...16334...363693...211755....3708666....1743841
%C A201451 .4.110..844..1720...45532..363693..1129682..1136762...16354832...80822317
%C A201451 .1..32..426..4193...32314..211755..1136762..5464208...23238776...89540916
%C A201451 .4.198.2478..8065..313710.3708666.16354832.23238776..458459214.3056235023
%C A201451 .6..41.5990.16693.1126721.1743841.80822317.89540916.3056235023.2605975384
%H A201451 R. H. Hardin, <a href="/A201451/b201451.txt">Table of n, a(n) for n = 1..312</a>
%F A201451 T(n,1) = binomial(4,n modulo 4). For a 0..z array, T(n,1) = binomial(z+1, n modulo (z+1)).
%e A201451 Some solutions for n=10 k=3
%e A201451 ..0..0..0....0..0..0....0..0..1....0..0..1....0..0..0....0..1..1....0..0..1
%e A201451 ..0..1..1....0..0..1....0..0..2....0..0..1....0..0..0....0..1..1....0..0..2
%e A201451 ..0..1..2....0..1..1....0..0..2....0..0..2....0..1..1....0..1..1....0..1..2
%e A201451 ..0..1..2....0..1..1....0..1..2....0..1..2....1..1..2....0..1..2....0..1..2
%e A201451 ..0..1..2....1..1..2....1..1..3....0..1..2....1..2..3....0..2..2....0..1..3
%e A201451 ..1..1..3....2..2..2....1..1..3....1..2..2....1..2..3....0..2..2....1..2..3
%e A201451 ..1..2..3....2..2..3....1..1..3....1..3..3....1..2..3....0..3..3....1..2..3
%e A201451 ..2..2..3....2..2..3....2..2..3....1..3..3....1..2..3....2..3..3....1..2..3
%e A201451 ..2..2..3....3..3..3....2..2..3....2..3..3....2..3..3....2..3..3....1..3..3
%e A201451 ..3..3..3....3..3..3....2..3..3....2..3..3....2..3..3....2..3..3....2..3..3
%K A201451 nonn,tabl
%O A201451 1,1
%A A201451 _R. H. Hardin_ Dec 01 2011