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%I #8 Dec 10 2018 08:55:00
%S 3,9,19,19,268,1249,3140,5986,9792,14558,20284,26970,34616,43222,
%T 52788,63314,74800,87246,100652,115018,130344,146630,163876,182082,
%U 201248,221374,242460,264506,287512,311478,336404,362290,389136,416942,445708
%N Number of n X 4 nonnegative integer arrays with upper left 0 and lower right its king-move distance away minus 2 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="/A253219/b253219.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 480*n^2 - 4354*n + 10098 for n>6.
%F Conjectures from _Colin Barker_, Dec 10 2018: (Start)
%F G.f.: x*(3 + x^2 - 14*x^3 + 259*x^4 + 483*x^5 + 178*x^6 + 45*x^7 + 5*x^8) / (1 - x)^3.
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>9.
%F (End)
%e Some solutions for n=4:
%e ..0..0..0..1....0..0..1..1....0..0..0..1....0..0..0..1....0..0..0..1
%e ..0..0..1..1....0..1..1..1....0..0..1..1....0..0..0..1....0..0..0..1
%e ..1..1..1..1....1..1..1..1....0..0..1..1....0..0..1..1....1..1..1..1
%e ..1..1..1..1....1..1..1..1....1..1..1..1....1..1..1..1....1..1..1..1
%Y Column 4 of A253223.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 29 2014
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