A252924 - OEIS

%I #9 Nov 22 2015 13:19:41

%S 0,0,0,1,19,120,483,1500,3923,9069,19095,37356,68860,120835,203424,

%T 330525,520794,798830,1196562,1754859,2525385,3572722,4976785,6835554,

%U 9268149,12418275,16458065,21592350,28063386,36156069,46203670,58594123

%N 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 Column 2 of A252930.

%H R. H. Hardin, <a href="/A252924/b252924.txt">Table of n, a(n) for n = 1..210</a>

%F 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 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 Some solutions for n=6:

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

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

%e ..1..1....1..1....1..1....2..2....1..1....0..1....0..1....0..1....0..1....1..1

%e ..1..1....1..1....1..2....2..2....1..1....0..1....1..1....1..1....0..1....1..2

%e ..1..2....1..1....2..2....2..2....1..2....0..1....1..1....1..1....1..1....2..2

%e ..2..2....1..2....2..2....2..2....1..2....1..2....2..2....1..2....1..2....2..2

%K nonn

%O 1,5

%A _R. H. Hardin_, Dec 24 2014