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A213697 T(n,k)=Half the number of (n+1)X(n+1) symmetric 0..k arrays with no 2X2 subblock summing to 2k.

%I A213697 #6 Jul 22 2025 23:03:20
%S A213697 3,11,13,28,192,70,56,1320,7827,529,99,5470,208072,750261,5148,159,
%T A213697 17499,2322599,109820000,168382284,68798,240,45892,16537086,
%U A213697 4286833981,193946752094,88681187619,1220409,344,105856,84059234,83545858925
%N A213697 T(n,k)=Half the number of (n+1)X(n+1) symmetric 0..k arrays with no 2X2 subblock summing to 2k.
%C A213697 Table starts
%C A213697 .....3..........11...............28..................56....................99
%C A213697 ....13.........192.............1320................5470.................17499
%C A213697 ....70........7827...........208072.............2322599..............16537086
%C A213697 ...529......750261........109820000..........4286833981...........83545858925
%C A213697 ..5148...168382284.....193946752094......34389632236877......2256314178023600
%C A213697 .68798.88681187619.1146407046198040.1199143411128185584.325754552781442854792
%H A213697 R. H. Hardin, <a href="/A213697/b213697.txt">Table of n, a(n) for n = 1..73</a>
%e A213697 Some solutions for n=4 k=4
%e A213697 ..0..4..0..2..3....1..2..4..4..0....2..4..3..3..2....3..4..3..1..2
%e A213697 ..4..2..0..3..3....2..1..3..4..1....4..2..3..3..1....4..2..2..1..0
%e A213697 ..0..0..4..3..1....4..3..2..1..0....3..3..2..2..3....3..2..3..4..2
%e A213697 ..2..3..3..2..0....4..4..1..0..0....3..3..2..3..2....1..1..4..2..4
%e A213697 ..3..3..1..0..4....0..1..0..0..4....2..1..3..2..2....2..0..2..4..1
%Y A213697 Row 1 is A182260(n+1)
%K A213697 nonn,tabl
%O A213697 1,1
%A A213697 _R. H. Hardin_ Jun 18 2012