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A252871 Number of nX3 nonnegative integer arrays with upper left 0 and lower right n+3-4 and value increasing by 0 or 1 with every step right or down.

%I A252871 #9 Jul 23 2025 13:42:36
%S A252871 1,8,44,153,413,949,1948,3676,6497,10894,17492,27083,40653,59411,
%T A252871 84820,118630,162913,220100,293020,384941,499613,641313,814892,
%U A252871 1025824,1280257,1585066,1947908,2377279,2882573,3474143,4163364,4962698,5885761,6947392
%N A252871 Number of nX3 nonnegative integer arrays with upper left 0 and lower right n+3-4 and value increasing by 0 or 1 with every step right or down.
%C A252871 Column 3 of A252876
%H A252871 R. H. Hardin, <a href="/A252871/b252871.txt">Table of n, a(n) for n = 1..210</a>
%F A252871 Empirical: a(n) = (1/360)*n^6 + (1/20)*n^5 + (5/18)*n^4 + (1/3)*n^3 + (79/360)*n^2 - (113/60)*n + 2.
%F A252871 Empirical: G.f.: -x*(1+x+9*x^2-22*x^3+21*x^4-10*x^5+2*x^6) / (x-1)^7. - _R. J. Mathar_, Nov 23 2015
%e A252871 Some solutions for n=3
%e A252871 ..0..1..1....0..1..1....0..1..2....0..0..0....0..1..1....0..0..1....0..1..1
%e A252871 ..0..1..1....1..1..1....0..1..2....1..1..1....1..2..2....1..1..1....1..1..1
%e A252871 ..1..2..2....1..1..2....1..2..2....1..2..2....2..2..2....1..2..2....2..2..2
%K A252871 nonn
%O A252871 1,2
%A A252871 _R. H. Hardin_, Dec 24 2014