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A213962 T(n,k)=Number of n X n 0..k matrices with row and column i=1..n having sum <= i*k.

%I A213962 #7 Jul 22 2025 23:05:02
%S A213962 2,3,10,4,42,138,5,120,3186,5314,6,275,32060,1299735,575122,7,546,
%T A213962 199735,74323976,2860343784,176041978,8,980,909900,1839121115,
%U A213962 1494988224948,34107691901433,153143689594,9,1632,3323712,26346319032,214090209950060
%N A213962 T(n,k)=Number of n X n 0..k matrices with row and column i=1..n having sum <= i*k.
%C A213962 Table starts
%C A213962 ......2..........3.............4...............5.................6
%C A213962 .....10.........42...........120.............275...............546
%C A213962 ....138.......3186.........32060..........199735............909900
%C A213962 ...5314....1299735......74323976......1839121115.......26346319032
%C A213962 .575122.2860343784.1494988224948.214090209950060.13186531254708756
%H A213962 R. H. Hardin, <a href="/A213962/b213962.txt">Table of n, a(n) for n = 1..53</a>
%F A213962 Empirical: rows n=1,2,3,4 are polynomials of degree 1,4,9,16
%e A213962 Some solutions for n=4 k=4
%e A213962 ..0..1..1..0....4..0..0..0....1..3..0..0....3..0..1..0....4..0..0..0
%e A213962 ..2..4..1..1....0..4..4..0....0..4..2..1....1..2..0..3....0..2..2..3
%e A213962 ..0..1..2..4....0..3..4..2....0..1..0..1....0..3..1..2....0..0..1..2
%e A213962 ..0..0..1..3....0..0..1..1....1..0..4..0....0..2..1..0....0..0..3..0
%Y A213962 Row 2 is A108678
%K A213962 nonn,tabl
%O A213962 1,1
%A A213962 _R. H. Hardin_ Jun 28 2012