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A252872 Number of n X 4 nonnegative integer arrays with upper left 0 and lower right n+4-4 and value increasing by 0 or 1 with every step right or down.

%I A252872 #9 Feb 07 2019 11:32:36
%S A252872 3,26,153,615,1953,5281,12686,27805,56624,108549,197804,345216,580452,
%T A252872 944778,1494415,2304572,3474241,5131844,7441827,10612301,14903835,
%U A252872 20639511,28216356,38118271,50930582,67356343,88234526,114560238
%N A252872 Number of n X 4 nonnegative integer arrays with upper left 0 and lower right n+4-4 and value increasing by 0 or 1 with every step right or down.
%H A252872 R. H. Hardin, <a href="/A252872/b252872.txt">Table of n, a(n) for n = 1..210</a>
%F A252872 Empirical: a(n) = (1/8064)*n^8 + (1/288)*n^7 + (103/2880)*n^6 + (17/90)*n^5 + (655/1152)*n^4 + (331/288)*n^3 - (677/1120)*n^2 - (41/120)*n + 2.
%F A252872 Empirical: G.f.: -x*(3-x+27*x^2-78*x^3+120*x^4-110*x^5+59*x^6-17*x^7+2*x^8) / (x-1)^9. - _R. J. Mathar_, Nov 23 2015
%e A252872 Some solutions for n=3
%e A252872 ..0..0..1..1....0..0..0..1....0..0..1..1....0..1..1..2....0..1..1..1
%e A252872 ..0..0..1..2....0..0..1..2....0..1..2..2....0..1..2..2....0..1..1..2
%e A252872 ..1..1..2..3....0..1..2..3....1..2..3..3....0..1..2..3....1..1..2..3
%Y A252872 Column 4 of A252876.
%K A252872 nonn
%O A252872 1,1
%A A252872 _R. H. Hardin_, Dec 24 2014