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A220205 Number of 2 X n arrays of the minimum value of corresponding elements and their horizontal, vertical or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..3 2 X n array. 1

%I

%S 4,10,36,89,182,333,567,918,1431,2164,3190,4599,6500,9023,12321,16572,

%T 21981,28782,37240,47653,60354,75713,94139,116082,142035,172536,

%U 208170,249571,297424,352467,415493,487352,568953,661266,765324,882225,1013134

%N Number of 2 X n arrays of the minimum value of corresponding elements and their horizontal, vertical or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..3 2 X n array.

%C Row 2 of A220204.

%H R. H. Hardin, <a href="/A220205/b220205.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/60)*n^5 - (1/8)*n^4 + (11/6)*n^3 - (7/8)*n^2 + (3/20)*n for n>1.

%F Conjectures from _Colin Barker_, Jul 31 2018: (Start)

%F G.f.: x*(4 - 14*x + 36*x^2 - 57*x^3 + 48*x^4 - 18*x^5 + 3*x^6) / (1 - x)^6.

%F a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>7.

%F (End)

%e Some solutions for n=3:

%e ..1..0..0....3..0..0....0..0..1....0..0..0....0..0..0....2..0..0....0..0..0

%e ..3..0..0....3..0..0....0..0..0....3..0..0....1..0..0....3..0..0....0..0..0

%Y Cf. A220204.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 07 2012

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Last modified August 4 19:41 EDT 2020. Contains 336202 sequences. (Running on oeis4.)