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A253218 Number of n X 3 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 A253218 #8 Dec 09 2018 09:10:19
%S A253218 1,1,1,19,102,263,504,825,1226,1707,2268,2909,3630,4431,5312,6273,
%T A253218 7314,8435,9636,10917,12278,13719,15240,16841,18522,20283,22124,24045,
%U A253218 26046,28127,30288,32529,34850,37251,39732,42293,44934,47655,50456,53337,56298
%N A253218 Number of n X 3 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 A253218 R. H. Hardin, <a href="/A253218/b253218.txt">Table of n, a(n) for n = 1..210</a>
%F A253218 Empirical: a(n) = 40*n^2 - 279*n + 497 for n>4.
%F A253218 Conjectures from _Colin Barker_, Dec 09 2018: (Start)
%F A253218 G.f.: x*(1 - 2*x + x^2 + 18*x^3 + 47*x^4 + 13*x^5 + 2*x^6) / (1 - x)^3.
%F A253218 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>7.
%F A253218 (End)
%e A253218 Some solutions for n=4:
%e A253218 ..0..0..0....0..0..0....0..0..0....0..0..0....0..0..1....0..1..1....0..0..1
%e A253218 ..0..0..1....0..0..0....0..0..1....0..0..1....0..0..1....0..1..1....0..0..1
%e A253218 ..0..0..1....0..1..1....0..1..1....1..1..1....1..1..1....1..1..1....0..0..1
%e A253218 ..1..1..1....1..1..1....1..1..1....1..1..1....1..1..1....1..1..1....1..1..1
%Y A253218 Column 3 of A253223.
%K A253218 nonn
%O A253218 1,4
%A A253218 _R. H. Hardin_, Dec 29 2014