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A252973 Number of nX5 nonnegative integer arrays with upper left 0 and lower right n+5-5 and value increasing by 0 or 1 with every step right or down.

%I A252973 #6 Jul 23 2025 13:49:24
%S A252973 4,61,770,6997,46812,248182,1100210,4230324,14477724,44951694,
%T A252973 128484004,341970798,855386126,2025957453,4571859908,9881224135,
%U A252973 20544547580,41246142411,80218821614,151563108019,278867435440,500751223536
%N A252973 Number of nX5 nonnegative integer arrays with upper left 0 and lower right n+5-5 and value increasing by 0 or 1 with every step right or down.
%C A252973 Column 5 of A252976
%H A252973 R. H. Hardin, <a href="/A252973/b252973.txt">Table of n, a(n) for n = 1..210</a>
%F A252973 Empirical: a(n) = (29/130767436800)*n^15 + (29/1743565824)*n^14 + (761/1437004800)*n^13 + (4567/479001600)*n^12 + (156803/1437004800)*n^11 + (12553/14515200)*n^10 + (4753991/914457600)*n^9 + (7470857/304819200)*n^8 + (5376871/65318400)*n^7 + (1929223/10886400)*n^6 + (43011707/179625600)*n^5 + (2111353/19958400)*n^4 + (648195787/454053600)*n^3 + (11630747/16816800)*n^2 + (39227/9240)*n - 3
%e A252973 Some solutions for n=4
%e A252973 ..0..1..1..1..1....0..1..1..1..1....0..1..2..2..3....0..1..2..2..2
%e A252973 ..0..1..2..2..2....0..1..2..2..2....1..1..2..2..3....0..1..2..2..3
%e A252973 ..1..2..2..3..3....1..2..3..3..3....1..2..2..3..4....1..1..2..3..4
%e A252973 ..1..2..2..3..4....2..3..3..3..4....2..2..3..4..4....2..2..3..4..4
%K A252973 nonn
%O A252973 1,1
%A A252973 _R. H. Hardin_, Dec 25 2014