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%I #8 Dec 07 2018 11:51:06
%S 2,5,13,34,83,176,329,558,879,1308,1861,2554,3403,4424,5633,7046,8679,
%T 10548,12669,15058,17731,20704,23993,27614,31583,35916,40629,45738,
%U 51259,57208,63601,70454,77783,85604,93933,102786,112179,122128,132649,143758
%N Number of n X 2 nonnegative integer arrays with upper left 0 and every value within 3 of its king move distance from the upper left and every value increasing by 0 or 1 with every step right, diagonally se or down.
%H R. H. Hardin, <a href="/A252932/b252932.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (8/3)*n^3 - 18*n^2 + (145/3)*n - 42 for n>2.
%F Conjectures from _Colin Barker_, Dec 07 2018: (Start)
%F G.f.: x*(2 - 3*x + 5*x^2 + 4*x^3 + 7*x^4 + x^5) / (1 - x)^4.
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>6.
%F (End)
%e Some solutions for n=4:
%e ..0..0....0..1....0..0....0..0....0..0....0..0....0..1....0..1....0..0....0..0
%e ..1..1....1..1....1..1....1..1....0..1....0..1....0..1....0..1....0..0....0..0
%e ..1..1....2..2....2..2....1..2....1..1....0..1....0..1....0..1....0..1....0..0
%e ..1..1....2..2....3..3....2..2....2..2....1..1....0..1....1..1....0..1....0..0
%Y Column 2 of A252938.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 24 2014
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