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%I #7 Mar 20 2018 10:17:07
%S 6,41,266,1247,4657,67537,433401,1481460,3510600,6637020,10878576,
%T 16235268,22707096,30294060,38996160,48813396,59745768,71793276,
%U 84955920,99233700,114626616,131134668,148757856,167496180,187349640,208318236
%N Number of n X 5 nonnegative integer arrays with upper left 0 and lower right its king-move distance away minus 2 and every value increasing by 0 or 1 with every step right, diagonally se or down.
%C Column 5 of A252983.
%H R. H. Hardin, <a href="/A252980/b252980.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 557568*n^2 - 7467372*n + 25553940 for n>8.
%F Conjectures from _Colin Barker_, Mar 20 2018: (Start)
%F G.f.: x*(6 + 23*x + 161*x^2 + 566*x^3 + 1673*x^4 + 57041*x^5 + 243514*x^6 + 379211*x^7 + 298886*x^8 + 116199*x^9 + 17856*x^10) / (1 - x)^3.
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>11.
%F (End)
%e Some solutions for n=4:
%e ..0..0..1..1..2....0..0..0..0..1....0..0..0..0..0....0..1..1..1..1
%e ..0..0..1..1..2....1..1..1..1..1....0..1..1..1..1....0..1..1..1..1
%e ..1..1..1..1..2....1..1..1..1..2....1..1..1..2..2....0..1..1..1..1
%e ..1..1..1..1..2....1..2..2..2..2....1..1..2..2..2....0..1..2..2..2
%Y Cf. A252983.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 25 2014
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