%I
%S 8,34,153,711,3067,10920,30818,70640,138558,242764,391450,592808,
%T 855030,1186308,1594834,2088800,2676398,3365820,4165258,5082904,
%U 6126950,7305588,8627010,10099408,11730974,13529900,15504378,17662600,20012758,22563044
%N Number of n X 4 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 R. H. Hardin, <a href="/A252934/b252934.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (4096/3)*n^3  18720*n^2 + (269642/3)*n  149376 for n>6.
%F Conjectures from _Colin Barker_, Dec 07 2018: (Start)
%F G.f.: x*(8 + 2*x + 65*x^2 + 271*x^3 + 1013*x^4 + 2340*x^5 + 2849*x^6 + 1331*x^7 + 293*x^8 + 20*x^9) / (1  x)^4.
%F a(n) = 4*a(n1)  6*a(n2) + 4*a(n3)  a(n4) for n>10.
%F (End)
%e Some solutions for n=4:
%e ..0..0..0..0....0..0..1..1....0..0..1..1....0..0..1..1....0..0..1..1
%e ..0..0..0..0....1..1..1..2....1..1..1..2....0..0..1..2....0..1..1..2
%e ..0..1..1..1....1..1..1..2....1..1..2..2....1..1..1..2....0..1..2..2
%e ..0..1..1..2....1..2..2..2....1..1..2..3....2..2..2..2....0..1..2..3
%Y Column 4 of A252938.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 24 2014
