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%I #7 Dec 07 2018 06:16:50
%S 16,85,529,3365,18528,78674,244131,569420,1070036,1750150,2610438,
%T 3650950,4871686,6272646,7853830,9615238,11556870,13678726,15980806,
%U 18463110,21125638,23968390,26991366,30194566,33577990,37141638,40885510
%N Number of n X 6 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="/A252834/b252834.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 90112*n^2 - 1032064*n + 3059590 for n>9.
%F Conjectures from _Colin Barker_, Dec 07 2018: (Start)
%F G.f.: x*(16 + 37*x + 322*x^2 + 2017*x^3 + 9935*x^4 + 32656*x^5 + 60328*x^6 + 54521*x^7 + 15495*x^8 + 4171*x^9 + 676*x^10 + 50*x^11) / (1 - x)^3.
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>12.
%F (End)
%e Some solutions for n=4:
%e ..0..0..1..1..2..3....0..1..2..2..3..4....0..1..2..3..3..3....0..1..2..2..3..4
%e ..0..1..1..2..2..3....1..1..2..3..3..4....1..1..2..3..3..3....1..1..2..2..3..4
%e ..1..1..1..2..2..3....1..1..2..3..3..4....1..2..2..3..3..3....1..2..2..3..3..4
%e ..1..1..1..2..2..3....1..2..2..3..4..4....2..2..3..3..3..4....1..2..3..3..3..4
%Y Column 6 of A252836.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 22 2014
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