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A253220 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 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.

%I A253220 #8 Dec 10 2018 08:54:52
%S A253220 6,25,102,268,268,3568,16028,40238,77063,126673,189083,264293,352303,
%T A253220 453113,566723,693133,832343,984353,1149163,1326773,1517183,1720393,
%U A253220 1936403,2165213,2406823,2661233,2928443,3208453,3501263,3806873,4125283
%N A253220 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 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 A253220 R. H. Hardin, <a href="/A253220/b253220.txt">Table of n, a(n) for n = 1..210</a>
%F A253220 Empirical: a(n) = 6400*n^2 - 71990*n + 206573 for n>8.
%F A253220 Conjectures from _Colin Barker_, Dec 10 2018: (Start)
%F A253220 G.f.: x*(6 + 7*x + 45*x^2 + 31*x^3 - 255*x^4 + 3466*x^5 + 5860*x^6 + 2590*x^7 + 865*x^8 + 170*x^9 + 15*x^10) / (1 - x)^3.
%F A253220 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>11.
%F A253220 (End)
%e A253220 Some solutions for n=4:
%e A253220 ..0..1..1..1..2....0..1..1..2..2....0..0..0..1..2....0..0..0..1..2
%e A253220 ..1..1..1..1..2....0..1..1..2..2....0..0..0..1..2....1..1..1..1..2
%e A253220 ..1..1..2..2..2....1..1..2..2..2....0..1..1..1..2....1..1..2..2..2
%e A253220 ..1..2..2..2..2....2..2..2..2..2....1..1..2..2..2....2..2..2..2..2
%Y A253220 Column 5 of A253223.
%K A253220 nonn
%O A253220 1,1
%A A253220 _R. H. Hardin_, Dec 29 2014