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A201277 T(n,k) = number of n X k 0..2 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.

%I A201277 #15 Mar 18 2024 12:35:20
%S A201277 3,3,3,1,5,1,3,4,4,3,3,12,7,12,3,1,16,14,14,16,1,3,9,21,85,21,9,3,3,
%T A201277 27,41,199,199,41,27,3,1,33,54,143,556,143,54,33,1,3,16,86,740,442,
%U A201277 442,740,86,16,3,3,48,120,1274,2827,1260,2827,1274,120,48,3,1,56,168,759,5680
%N A201277 T(n,k) = number of n X k 0..2 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.
%C A201277 Table starts
%C A201277 .3..3...1....3.....3.....1......3.......3.......1........3........3........1
%C A201277 .3..5...4...12....16.....9.....27......33......16.......48.......56.......25
%C A201277 .1..4...7...14....21....41.....54......86.....120......168......218......307
%C A201277 .3.12..14...85...199...143....740....1274.....759.....3416.....5312.....2746
%C A201277 .3.16..21..199...556...442...2827....5680....3651....19960....35039....19820
%C A201277 .1..9..41..143...442..1260...3113....7331...15969....32737....63942...120318
%C A201277 .3.27..54..740..2827..3113..27008...71704...59070...408600...894812...621910
%C A201277 .3.33..86.1274..5680..7331..71704..215577..200867..1537010..3717215..2850024
%C A201277 .1.16.120..759..3651.15969..59070..200867..613916..1755850..4655000.11705266
%C A201277 .3.48.168.3416.19960.32737.408600.1537010.1755850.16442049.47956581.43851889
%H A201277 R. H. Hardin, <a href="/A201277/b201277.txt">Table of n, a(n) for n = 1..684</a>
%F A201277 T(n,1) = binomial(3,n modulo 3). For a 0..z array, T(n,1) = binomial(z+1, n modulo (z+1)).
%e A201277 Some solutions for n=7 k=5
%e A201277 ..0..0..0..0..0....0..0..0..0..0....0..0..0..0..0....0..0..0..0..1
%e A201277 ..0..0..0..1..1....0..0..0..0..1....0..0..0..0..2....0..0..0..1..1
%e A201277 ..0..1..1..1..1....0..0..1..1..1....0..0..0..1..2....0..0..0..1..2
%e A201277 ..0..1..2..2..2....1..1..2..2..2....1..1..1..1..2....0..0..1..2..2
%e A201277 ..0..1..2..2..2....1..1..2..2..2....1..1..1..2..2....1..1..1..2..2
%e A201277 ..0..1..2..2..2....1..1..2..2..2....1..1..2..2..2....1..1..2..2..2
%e A201277 ..1..1..2..2..2....1..1..2..2..2....1..2..2..2..2....1..2..2..2..2
%Y A201277 Columns k=1-7 give: A169609, A201271, A201272, A201273, A201274, A201275, A201276.
%Y A201277 Main diagonal gives A201270.
%K A201277 nonn,tabl
%O A201277 1,1
%A A201277 _R. H. Hardin_, Nov 29 2011