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Number of (n+1) X (n+1) 0..2 arrays colored with the upper median value of each 2 X 2 subblock.
1

%I #9 Oct 20 2018 06:04:48

%S 81,722,1494,2356,5358,10420,21288,49860,114312,228100,449256,1104660,

%T 2526024,5184100,9904296,25347060,57842184,121308100,226373736,

%U 597365460,1361119944,2899992100,5319604776,14353159860,32669044104,70376436100

%N Number of (n+1) X (n+1) 0..2 arrays colored with the upper median value of each 2 X 2 subblock.

%H R. H. Hardin, <a href="/A235946/b235946.txt">Table of n, a(n) for n = 1..36</a>

%F Empirical: a(n) = 41*a(n-4) -400*a(n-8) for n>13.

%F Empirical g.f.: x*(81 + 722*x + 1494*x^2 + 2356*x^3 + 2037*x^4 - 19182*x^5 - 39966*x^6 - 46736*x^7 - 72966*x^8 + 89680*x^9 + 174048*x^10 + 2800*x^11 - 17568*x^12) / ((1 - 2*x)*(1 + 2*x)*(1 + 4*x^2)*(1 - 5*x^2)*(1 + 5*x^2)). - _Colin Barker_, Oct 20 2018

%e Some solutions for n=5:

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

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

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

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

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

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

%Y Diagonal of A235954.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 17 2014