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Number of (n+1)X3 0..2 arrays with rows and columns in nondecreasing order and with no 2X2 subblock sum differing from a horizontal or vertical neighbor subblock sum by more than one
1

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

%S 58,74,239,578,1599,4233,11128,28248,67622,152873,327044,665356,

%T 1293389,2411872,4330976,7515107,12640705,20668977,32935784,51260994,

%U 78079741,116598158,170976280,246540941,350031617,489882295,676542576,922841348

%N Number of (n+1)X3 0..2 arrays with rows and columns in nondecreasing order and with no 2X2 subblock sum differing from a horizontal or vertical neighbor subblock sum by more than one

%C Column 2 of A184081

%H R. H. Hardin, <a href="/A184074/b184074.txt">Table of n, a(n) for n = 1..200</a>

%e Some solutions for 4X3

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

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

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

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

%e ...

%e ...5..5.......5..6.......6..7.......5..6.......2..3.......2..3.......3..4...

%e ...6..5.......5..5.......6..6.......6..5.......3..2.......2..3.......4..3...

%K nonn

%O 1,1

%A _R. H. Hardin_ Jan 09 2011