%I #6 Nov 03 2022 21:46:15

%S 16,147,1032,5490,23664,86724,279300,809349,2147638,5289321,12219498,

%T 26705926,55598468,110890224,212893984,395014703,710759820,1243830839,

%U 2122388828,3538891338,5777267504,9249641452,14545342212,22495562705

%N Number of n X 6 nonnegative integer arrays with upper left 0 and every value within 2 of its city block distance from the upper left and every value increasing by 0 or 1 with every step right or down.

%C Column 6 of A252820.

%H R. H. Hardin, <a href="/A252818/b252818.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/11404800)*n^12 + (1/211200)*n^11 + (37/345600)*n^10 + (143/103680)*n^9 + (27977/2419200)*n^8 + (83399/1209600)*n^7 + (319693/1036800)*n^6 + (34283/34560)*n^5 + (59941/28800)*n^4 + (482543/129600)*n^3 + (720359/277200)*n^2 + (44551/13860)*n + 3.

%e Some solutions for n=4

%e ..0..1..2..3..4..5....0..1..2..3..4..5....0..1..2..3..3..4....0..1..2..2..3..4

%e ..1..2..2..3..4..5....1..2..3..4..4..5....1..2..3..4..4..5....1..2..2..2..3..4

%e ..2..3..3..3..4..5....2..2..3..4..5..5....1..2..3..4..5..5....2..3..3..3..4..5

%e ..3..3..3..4..5..6....3..3..4..5..5..6....1..2..3..4..5..6....3..4..4..4..5..6

%Y Cf. A252820.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 22 2014