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%I #6 Nov 23 2015 13:53:14
%S 0,1,33,615,6997,53950,315198,1499394,6083808,21733215,69921908,
%T 206052448,563440284,1444285973,3499040581,8065603025,17787652381,
%U 37705694442,77126966988,152747362302,293741640632,549886035657
%N Number of nX4 nonnegative integer arrays with upper left 0 and lower right n+4-6 and value increasing by 0 or 1 with every step right or down
%C Column 4 of A252930
%H R. H. Hardin, <a href="/A252926/b252926.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (13/1609445376000)*n^16 + (13/18289152000)*n^15 + (3947/149448499200)*n^14 + (20057/37362124800)*n^13 + (728009/114960384000)*n^12 + (312437/7185024000)*n^11 + (1303193/7315660800)*n^10 + (848039/1828915200)*n^9 + (11500417/20901888000)*n^8 - (1346209/373248000)*n^7 - (14478857/1149603840)*n^6 - (361673/8164800)*n^5 + (13716552599/33530112000)*n^4 + (454863863/1397088000)*n^3 - (207327073/86486400)*n^2 + (137883/80080)*n.
%F Empirical: G.f.: x^2*(-1 -16*x -190*x^2 -350*x^3 +1419*x^4 -3792*x^5 +7860*x^6 -11238*x^7 +11247*x^8 -8133*x^9 +4280*x^10 -1600*x^11 +401*x^12 -60*x^13+4*x^14) / (x-1)^17 . - _R. J. Mathar_, Nov 23 2015
%e Some solutions for n=4
%e ..0..0..1..2....0..0..0..0....0..0..1..1....0..1..1..1....0..1..1..1
%e ..0..1..1..2....0..0..0..1....1..1..1..1....0..1..1..2....1..1..1..2
%e ..1..1..1..2....0..0..1..2....1..1..1..1....1..1..1..2....1..1..1..2
%e ..1..1..2..2....0..0..1..2....2..2..2..2....1..1..2..2....1..1..2..2
%K nonn
%O 1,3
%A _R. H. Hardin_, Dec 24 2014
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