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%I #8 Dec 06 2018 20:06:47
%S 4,13,44,127,288,529,850,1251,1732,2293,2934,3655,4456,5337,6298,7339,
%T 8460,9661,10942,12303,13744,15265,16866,18547,20308,22149,24070,
%U 26071,28152,30313,32554,34875,37276,39757,42318,44959,47680,50481,53362,56323
%N Number of n X 3 nonnegative integer arrays with upper left 0 and every value within 2 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="/A252831/b252831.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 40*n^2 - 199*n + 283 for n>3.
%F Conjectures from _Colin Barker_, Dec 06 2018: (Start)
%F G.f.: x*(4 + x + 17*x^2 + 30*x^3 + 26*x^4 + 2*x^5) / (1 - x)^3.
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>6.
%F (End)
%e Some solutions for n=4:
%e ..0..1..2....0..0..0....0..1..1....0..1..1....0..1..2....0..0..1....0..0..0
%e ..0..1..2....0..0..1....1..1..2....1..1..1....1..1..2....1..1..1....0..0..1
%e ..1..1..2....1..1..1....1..1..2....1..2..2....2..2..2....1..1..2....0..1..1
%e ..2..2..2....2..2..2....1..2..2....1..2..3....3..3..3....1..1..2....1..1..2
%Y Column 3 of A252836.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 22 2014
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