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1/8 the number of (n+1)X4 0..3 arrays with all 2X2 subblock sums the same
1

%I #5 Mar 31 2012 12:35:56

%S 242,491,1052,2597,6650,18701,53948,165929,520322,1709981,5706212,

%T 19735097,69075290,248513021,902117708,3343884089,12473559602,

%U 47261525021,179833241972,692191519097,2671565177930,10398142103741

%N 1/8 the number of (n+1)X4 0..3 arrays with all 2X2 subblock sums the same

%C Column 3 of A184029

%H R. H. Hardin, <a href="/A184023/b184023.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n)=8*a(n-1)+16*a(n-2)-268*a(n-3)+189*a(n-4)+3388*a(n-5)-5824*a(n-6)-20048*a(n-7)+49756*a(n-8)+52752*a(n-9)-196896*a(n-10)-24192*a(n-11)+369216*a(n-12)-131328*a(n-13)-262656*a(n-14)+165888*a(n-15)

%e Some solutions for 6X4

%e ..2..1..2..1....1..2..1..2....1..1..1..1....1..3..1..2....1..1..3..2

%e ..2..1..2..1....1..2..1..2....2..1..2..1....2..1..2..2....2..1..0..0

%e ..0..3..0..3....2..1..2..1....1..1..1..1....1..3..1..2....1..1..3..2

%e ..3..0..3..0....0..3..0..3....2..1..2..1....3..0..3..1....2..1..0..0

%e ..2..1..2..1....2..1..2..1....1..1..1..1....1..3..1..2....0..2..2..3

%e ..0..3..0..3....1..2..1..2....1..2..1..2....2..1..2..2....2..1..0..0

%K nonn

%O 1,1

%A _R. H. Hardin_ Jan 08 2011