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A252924 Number of n X 2 nonnegative integer arrays with upper left 0 and lower right n+2-6 and value increasing by 0 or 1 with every step right or down.

%I A252924 #9 Nov 22 2015 13:19:41
%S A252924 0,0,0,1,19,120,483,1500,3923,9069,19095,37356,68860,120835,203424,
%T A252924 330525,520794,798830,1196562,1754859,2525385,3572722,4976785,6835554,
%U A252924 9268149,12418275,16458065,21592350,28063386,36156069,46203670,58594123
%N A252924 Number of n X 2 nonnegative integer arrays with upper left 0 and lower right n+2-6 and value increasing by 0 or 1 with every step right or down.
%C A252924 Column 2 of A252930.
%H A252924 R. H. Hardin, <a href="/A252924/b252924.txt">Table of n, a(n) for n = 1..210</a>
%F A252924 Empirical: a(n) = (1/40320)*n^8 + (1/1120)*n^7 + (7/2880)*n^6 - (1/16)*n^5 + (647/5760)*n^4 + (87/160)*n^3 - (21317/10080)*n^2 + (141/56)*n - 1.
%F A252924 Empirical: G.f.: x^4*(-1-10*x+15*x^2-3*x^3-3*x^4+x^5) / (x-1)^9 . - _R. J. Mathar_, Nov 21 2015
%e A252924 Some solutions for n=6:
%e A252924 ..0..0....0..0....0..1....0..0....0..0....0..1....0..0....0..0....0..1....0..0
%e A252924 ..0..1....1..1....1..1....1..1....0..0....0..1....0..1....0..0....0..1....1..1
%e A252924 ..1..1....1..1....1..1....2..2....1..1....0..1....0..1....0..1....0..1....1..1
%e A252924 ..1..1....1..1....1..2....2..2....1..1....0..1....1..1....1..1....0..1....1..2
%e A252924 ..1..2....1..1....2..2....2..2....1..2....0..1....1..1....1..1....1..1....2..2
%e A252924 ..2..2....1..2....2..2....2..2....1..2....1..2....2..2....1..2....1..2....2..2
%K A252924 nonn
%O A252924 1,5
%A A252924 _R. H. Hardin_, Dec 24 2014