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Number of 4Xn arrays of the minimum value of corresponding elements and their horizontal, diagonal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..1 4Xn array
1

%I #4 Nov 21 2012 05:13:04

%S 5,9,22,68,166,380,821,1700,3374,6430,11784,20830,35631,59161,95611,

%T 150769,232486,351241,520819,759117,1089094,1539882,2148076,2959222,

%U 4029523,5427784,7237618,9559936,12515745,16249279,20931489,26763919

%N Number of 4Xn arrays of the minimum value of corresponding elements and their horizontal, diagonal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..1 4Xn array

%C Row 4 of A219519

%H R. H. Hardin, <a href="/A219521/b219521.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/40320)*n^8 - (1/3360)*n^7 + (7/576)*n^6 - (7/60)*n^5 + (1567/5760)*n^4 + (2201/160)*n^3 - (116111/672)*n^2 + (251961/280)*n - 1757 for n>9

%e Some solutions for n=3

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_ Nov 21 2012