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A229794 T(n,k)=Number of n X n 0..k arrays with rows and columns in lexicographically nondecreasing order.

%I A229794 #8 Jul 23 2025 05:47:18
%S A229794 2,3,7,4,29,45,5,86,1169,650,6,205,14178,250841,24520,7,421,102251,
%T A229794 21907055,318174607,2625117,8,777,520017,733861607,348053502590,
%U A229794 2533164987353,836488618,9,1324,2066505,13111482259,83399309397669
%N A229794 T(n,k)=Number of n X n 0..k arrays with rows and columns in lexicographically nondecreasing order.
%C A229794 Table starts
%C A229794 .....2.........3............4..............5................6
%C A229794 .....7........29...........86............205..............421
%C A229794 ....45......1169........14178.........102251...........520017
%C A229794 ...650....250841.....21907055......733861607......13111482259
%C A229794 .24520.318174607.348053502590.83399309397669.7470491620551006
%H A229794 R. H. Hardin, <a href="/A229794/b229794.txt">Table of n, a(n) for n = 1..63</a>
%F A229794 Empirical for row n:
%F A229794 n=1: a(n) = 1*n + 1
%F A229794 n=2: a(n) = (1/3)*n^4 + (7/6)*n^3 + (13/6)*n^2 + (7/3)*n + 1
%F A229794 n=3: [polynomial of degree 9]
%F A229794 n=4: [polynomial of degree 16]
%e A229794 Some solutions for n=2 k=4
%e A229794 ..1..4....1..3....1..4....0..3....1..4....2..4....1..4....0..3....0..1....0..3
%e A229794 ..2..3....3..2....4..0....1..1....2..0....4..2....3..2....2..1....0..1....4..4
%Y A229794 Column 1 is A089006
%Y A229794 Column 2 is A162085
%Y A229794 Column 3 is A162086
%Y A229794 Column 4 is A162087
%Y A229794 Column 5 is A162088
%Y A229794 Column 6 is A162089
%Y A229794 Column 7 is A162090
%K A229794 nonn,tabl
%O A229794 1,1
%A A229794 _R. H. Hardin_, Sep 29 2013