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 A201101 T(n,k)=Number of nXk 0..7 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other 8

%I

%S 8,28,28,56,140,56,70,140,140,70,56,14,252,14,56,28,728,10423,10423,

%T 728,28,8,3696,6972,2490,6972,3696,8,1,3273,85005,905695,905695,85005,

%U 3273,1,8,323,478198,89311,1445712,89311,478198,323,8,28,10516,27782,31885648

%N T(n,k)=Number of nXk 0..7 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other

%C Table starts

%C ..8....28......56........70...........56.............28..............8

%C .28...140.....140........14..........728...........3696...........3273

%C .56...140.....252.....10423.........6972..........85005.........478198

%C .70....14...10423......2490.......905695..........89311.......31885648

%C .56...728....6972....905695......1445712.......55782998......945668958

%C .28..3696...85005.....89311.....55782998.....2244318652....12230511648

%C ..8..3273..478198..31885648....945668958....12230511648....80495995176

%C ..1...323...27782...2647438....123026475.....5732148226...155796077603

%C ..8.10516.3937944.656371640..46355746304..1359373604245.18098348588856

%C .28.37590.5383954..36544193.138881000080.28620297165083

%H R. H. Hardin, <a href="/A201101/b201101.txt">Table of n, a(n) for n = 1..126</a>

%F T(n,1) = binomial(8,n modulo 8). For a 0..z array, T(n,1) = binomial(z+1, n modulo (z+1)).

%e Some solutions for n=3 k=3

%e ..0..1..1....0..2..4....0..1..3....0..1..2....0..3..6....0..2..3....0..1..5

%e ..2..4..5....1..3..6....2..5..7....0..4..5....1..4..7....1..4..6....2..3..6

%e ..3..6..7....1..5..7....4..6..7....3..6..7....2..5..7....2..5..7....4..4..7

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Nov 26 2011

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Last modified May 20 06:37 EDT 2022. Contains 353852 sequences. (Running on oeis4.)