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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
2

%I #8 Nov 23 2015 04:51:04

%S 0,0,1,13,61,192,483,1050,2058,3732,6369,10351,16159,24388,35763,

%T 51156,71604,98328,132753,176529,231553,299992,384307,487278,612030,

%U 762060,941265,1153971,1404963,1699516,2043427,2443048,2905320,3437808,4048737

%N 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 Column 2 of A252976

%H R. H. Hardin, <a href="/A252970/b252970.txt">Table of n, a(n) for n = 1..210</a>

%F 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 Empirical: G.f.: -x^3*(1+6*x-9*x^2+3*x^3) / (x-1)^7 . - _R. J. Mathar_, Nov 23 2015

%e Some solutions for n=4

%e ..0..0....0..0....0..0....0..0....0..0....0..0....0..1....0..0....0..1....0..1

%e ..0..1....0..0....0..0....1..1....0..0....0..1....0..1....0..0....1..1....0..1

%e ..0..1....0..0....0..0....1..1....1..1....0..1....0..1....0..1....1..1....0..1

%e ..1..1....0..1....1..1....1..1....1..1....0..1....0..1....0..1....1..1....1..1

%K nonn

%O 1,4

%A _R. H. Hardin_, Dec 25 2014