%I #7 Dec 06 2018 16:36:54
%S 7,29,127,493,1474,3365,6211,10017,14783,20509,27195,34841,43447,
%T 53013,63539,75025,87471,100877,115243,130569,146855,164101,182307,
%U 201473,221599,242685,264731,287737,311703,336629,362515,389361,417167,445933
%N Number of n X 4 nonnegative integer arrays with upper left 0 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="/A252832/b252832.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 480*n^2 - 3394*n + 6449 for n>5.
%F Conjectures from _Colin Barker_, Dec 06 2018: (Start)
%F G.f.: x*(7 + 8*x + 61*x^2 + 192*x^3 + 347*x^4 + 295*x^5 + 45*x^6 + 5*x^7) / (1 - x)^3.
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>8.
%F (End)
%e Some solutions for n=4:
%e ..0..1..1..1....0..0..1..1....0..1..1..2....0..0..1..1....0..1..1..1
%e ..0..1..1..1....1..1..1..1....0..1..1..2....0..0..1..1....1..1..2..2
%e ..0..1..1..2....1..2..2..2....0..1..1..2....0..1..1..2....1..2..2..2
%e ..1..1..2..2....1..2..2..3....1..1..2..2....1..1..1..2....2..2..3..3
%Y Column 4 of A252836.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 22 2014