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A252933 Number of n X 3 nonnegative integer arrays with upper left 0 and every value within 3 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 A252933 #8 Dec 07 2018 11:51:20
%S A252933 4,13,44,153,494,1343,3016,5833,10114,16179,24348,34941,48278,64679,
%T A252933 84464,107953,135466,167323,203844,245349,292158,344591,402968,467609,
%U A252933 538834,616963,702316,795213,895974,1004919,1122368,1248641,1384058
%N A252933 Number of n X 3 nonnegative integer arrays with upper left 0 and every value within 3 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 A252933 R. H. Hardin, <a href="/A252933/b252933.txt">Table of n, a(n) for n = 1..210</a>
%F A252933 Empirical: a(n) = (160/3)*n^3 - 548*n^2 + (6071/3)*n - 2591 for n>4.
%F A252933 Conjectures from _Colin Barker_, Dec 07 2018: (Start)
%F A252933 G.f.: x*(4 - 3*x + 16*x^2 + 39*x^3 + 98*x^4 + 122*x^5 + 40*x^6 + 4*x^7) / (1 - x)^4.
%F A252933 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>8.
%F A252933 (End)
%e A252933 Some solutions for n=4:
%e A252933 ..0..0..0....0..0..1....0..1..1....0..0..1....0..0..0....0..0..0....0..0..0
%e A252933 ..0..0..1....1..1..1....1..1..1....0..1..1....0..0..0....0..0..1....0..0..1
%e A252933 ..0..1..1....1..2..2....2..2..2....1..1..1....1..1..1....0..0..1....1..1..1
%e A252933 ..0..1..1....1..2..2....2..2..3....1..1..2....1..1..1....1..1..1....1..1..2
%Y A252933 Column 3 of A252938.
%K A252933 nonn
%O A252933 1,1
%A A252933 _R. H. Hardin_, Dec 24 2014