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A252972 Number of nX4 nonnegative integer arrays with upper left 0 and lower right n+4-5 and value increasing by 0 or 1 with every step right or down.

%I A252972 #6 Jul 23 2025 13:49:17
%S A252972 1,13,153,1236,6997,30802,112877,359550,1024773,2667554,6438457,
%T A252972 14575914,31230978,63789948,124931040,235737421,430298389,762367687,
%U A252972 1314817821,2212837300,3642069999,5873199042,9294839027,14457028052,22128113529
%N A252972 Number of nX4 nonnegative integer arrays with upper left 0 and lower right n+4-5 and value increasing by 0 or 1 with every step right or down.
%C A252972 Column 4 of A252976
%H A252972 R. H. Hardin, <a href="/A252972/b252972.txt">Table of n, a(n) for n = 1..210</a>
%F A252972 Empirical: a(n) = (29/479001600)*n^12 + (29/8870400)*n^11 + (3083/43545600)*n^10 + (233/290304)*n^9 + (73739/14515200)*n^8 + (48151/2419200)*n^7 + (2494049/43545600)*n^6 + (31657/483840)*n^5 - (1169489/10886400)*n^4 - (1024151/1814400)*n^3 + (2116423/831600)*n^2 - (601/27720)*n - 1
%e A252972 Some solutions for n=4
%e A252972 ..0..1..1..1....0..1..2..3....0..0..0..1....0..1..2..2....0..0..1..2
%e A252972 ..0..1..1..1....0..1..2..3....1..1..1..2....0..1..2..2....0..1..2..2
%e A252972 ..0..1..2..2....1..2..2..3....2..2..2..2....1..1..2..3....1..2..2..2
%e A252972 ..0..1..2..3....1..2..3..3....2..2..3..3....1..2..2..3....2..3..3..3
%K A252972 nonn
%O A252972 1,2
%A A252972 _R. H. Hardin_, Dec 25 2014