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A213800 T(n,k)=Number of n X n 0..k symmetric arrays with every row summing to floor(n*k/2).

%I A213800 #7 Jun 02 2025 08:04:01
%S A213800 1,1,2,1,3,4,1,4,13,18,1,5,29,169,112,1,6,57,880,5673,1760,1,7,96,
%T A213800 3249,87932,526443,35150,1,8,153,9522,815263,34725760,133721189,
%U A213800 1944530,1,9,226,23753,4843626,932587453,46259653191,95133854529,133948836,1,10,323
%N A213800 T(n,k)=Number of n X n 0..k symmetric arrays with every row summing to floor(n*k/2).
%C A213800 Table starts
%C A213800 ...........1...............1...............1.............1...............1
%C A213800 ...........2...............3...............4.............5...............6
%C A213800 ...........4..............13..............29............57..............96
%C A213800 ..........18.............169.............880..........3249............9522
%C A213800 .........112............5673...........87932........815263.........4843626
%C A213800 ........1760..........526443........34725760.....932587453.....13937940952
%C A213800 .......35150.......133721189.....46259653191.4893373431575.212962858290086
%C A213800 .....1944530.....95133854529.250599609089536
%C A213800 ...133948836.190409704025737
%C A213800 .26615510712
%H A213800 R. H. Hardin, <a href="/A213800/b213800.txt">Table of n, a(n) for n = 1..62</a>
%e A213800 Some solutions for n=4 k=3
%e A213800 ..1..1..1..3....1..3..2..0....1..3..0..2....0..1..2..3....2..1..2..1
%e A213800 ..1..2..3..0....3..1..0..2....3..3..0..0....1..3..2..0....1..0..2..3
%e A213800 ..1..3..0..2....2..0..1..3....0..0..3..3....2..2..1..1....2..2..0..2
%e A213800 ..3..0..2..1....0..2..3..1....2..0..3..1....3..0..1..2....1..3..2..0
%K A213800 nonn,tabl
%O A213800 1,3
%A A213800 _R. H. Hardin_ Jun 20 2012