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A252970 Number of nX2 nonnegative integer arrays with upper left 0 and lower right n+2-5 and value increasing by 0 or 1 with every step right or down.

%I A252970 #10 Jul 23 2025 13:49:10
%S A252970 0,0,1,13,61,192,483,1050,2058,3732,6369,10351,16159,24388,35763,
%T A252970 51156,71604,98328,132753,176529,231553,299992,384307,487278,612030,
%U A252970 762060,941265,1153971,1404963,1699516,2043427,2443048,2905320,3437808,4048737
%N A252970 Number of nX2 nonnegative integer arrays with upper left 0 and lower right n+2-5 and value increasing by 0 or 1 with every step right or down.
%C A252970 Column 2 of A252976
%H A252970 R. H. Hardin, <a href="/A252970/b252970.txt">Table of n, a(n) for n = 1..210</a>
%F A252970 Empirical: a(n) = (1/720)*n^6 + (7/240)*n^5 - (1/144)*n^4 - (31/48)*n^3 + (271/180)*n^2 - (53/60)*n = n*(n-1)*(n-2)*(n^3+24*n^2+65*n-318)/720.
%F A252970 Empirical: G.f.: -x^3*(1+6*x-9*x^2+3*x^3) / (x-1)^7 . - _R. J. Mathar_, Nov 23 2015
%e A252970 Some solutions for n=4
%e A252970 ..0..0....0..0....0..0....0..0....0..0....0..0....0..1....0..0....0..1....0..1
%e A252970 ..0..1....0..0....0..0....1..1....0..0....0..1....0..1....0..0....1..1....0..1
%e A252970 ..0..1....0..0....0..0....1..1....1..1....0..1....0..1....0..1....1..1....0..1
%e A252970 ..1..1....0..1....1..1....1..1....1..1....0..1....0..1....0..1....1..1....1..1
%K A252970 nonn
%O A252970 1,4
%A A252970 _R. H. Hardin_, Dec 25 2014