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%I #7 Mar 31 2012 12:35:53
%S 85,325,325,1333,1001,1333,5725,3445,3445,5725,25405,12785,10213,
%T 12785,25405,115525,50125,33325,33325,50125,115525,535333,205001,
%U 116653,97145,116653,205001,535333,2517805,867205,431125,307525,307525,431125,867205
%N T(n,k)=Number of (n+1)X(k+1) 0..4 arrays with every 2X2 subblock summing to 8
%C Table starts
%C .......85......325......1333.....5725....25405...115525...535333..2517805
%C ......325.....1001......3445....12785....50125...205001...867205..3771425
%C .....1333.....3445.....10213....33325...116653...431125..1664533..6663805
%C .....5725....12785.....33325....97145...307525..1037585..3684925.13653545
%C ....25405....50125....116653...307525...889525..2764525..9103453.31446805
%C ...115525...205001....431125..1037585..2764525..7969001.24478885.79273025
%C ...535333...867205...1664533..3684925..9103453.24478885
%C ..2517805..3771425...6663805.13653545.31446805
%C .11982925.16784125..27510973.52436725
%C .57575125.76156601.116631205
%H R. H. Hardin, <a href="/A183652/b183652.txt">Table of n, a(n) for n = 1..84</a>
%F Empirical, for every row and column: a(n)=15*a(n-1)-85*a(n-2)+225*a(n-3)-274*a(n-4)+120*a(n-5)
%F The coefficient of a(n-i) is -s(6,6-i), s() being the Stirling number of the first kind, via D. S. McNeil and M. F. Hasler in the Sequence Fans Mailing List.
%F For a 0..z array with 2X2 blocks summing to 2z, the coefficients are -s(z+2,z+2-i)
%e Some solutions for 4X3
%e ..1..1..2....2..2..3....3..3..1....2..3..2....0..2..2....2..1..3....2..3..2
%e ..3..3..2....4..0..3....0..2..2....1..2..1....4..2..2....3..2..2....0..3..0
%e ..2..0..3....2..2..3....2..4..0....1..4..1....2..0..4....1..2..2....1..4..1
%e ..3..3..2....2..2..1....2..0..4....1..2..1....3..3..1....4..1..3....3..0..3
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Jan 06 2011
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