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A229774 T(n,k)=Number of n X n 0..k arrays with rows in lexicographically nondecreasing order and columns in nonincreasing order.

%I A229774 #7 Jul 23 2025 05:46:52
%S A229774 2,3,6,4,22,20,5,60,322,70,6,135,3232,12958,252,7,266,21331,1058494,
%T A229774 2179956,924,8,476,103222,35452250,3062815568,1976588468,3432,9,792,
%U A229774 397460,637396928,843211336888,90462380211862,10811999412826,12870,10
%N A229774 T(n,k)=Number of n X n 0..k arrays with rows in lexicographically nondecreasing order and columns in nonincreasing order.
%C A229774 Table starts
%C A229774 ...2..........3..............4..................5.....................6
%C A229774 ...6.........22.............60................135...................266
%C A229774 ..20........322...........3232..............21331................103222
%C A229774 ..70......12958........1058494...........35452250.............637396928
%C A229774 .252....2179956.....3062815568.......843211336888........81937334158292
%C A229774 .924.1976588468.90462380211862.322942973130396495.245200063296427870294
%H A229774 R. H. Hardin, <a href="/A229774/b229774.txt">Table of n, a(n) for n = 1..62</a>
%F A229774 Empirical for row n:
%F A229774 n=1: a(n) = n + 1
%F A229774 n=2: a(n) = (1/6)*n^4 + (5/6)*n^3 + (11/6)*n^2 + (13/6)*n + 1
%F A229774 n=3: [polynomial of degree 9]
%F A229774 n=4: [polynomial of degree 16]
%e A229774 Some solutions for n=3 k=4
%e A229774 ..2..2..0....3..3..3....2..1..1....1..0..0....1..1..0....2..0..0....2..2..2
%e A229774 ..3..0..0....4..0..0....3..0..0....1..3..0....3..0..3....2..2..2....3..3..1
%e A229774 ..4..3..3....4..2..0....3..4..4....2..4..1....4..4..1....2..2..2....4..4..0
%Y A229774 Column 1 is A000984
%Y A229774 Row 1 is A000027(n+1)
%Y A229774 Row 2 is A071239(n+1)
%K A229774 nonn,tabl
%O A229774 1,1
%A A229774 _R. H. Hardin_, Sep 29 2013