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A220045 Number of 2 X n 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 nonincreasing columns, 0..3 2 X n array. 1

%I

%S 10,13,25,50,90,152,249,397,618,941,1403,2050,2938,4134,5717,7779,

%T 10426,13779,17975,23168,29530,37252,46545,57641,70794,86281,104403,

%U 125486,149882,177970,210157,246879,288602,335823,389071,448908,515930,590768

%N Number of 2 X n 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 nonincreasing columns, 0..3 2 X n array.

%C Row 2 of A220044.

%H R. H. Hardin, <a href="/A220045/b220045.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/120)*n^5 - (1/24)*n^4 + (5/24)*n^3 + (109/24)*n^2 - (1063/60)*n + 39 for n>4.

%F Conjectures from _Colin Barker_, Jul 30 2018: (Start)

%F G.f.: x*(10 - 47*x + 97*x^2 - 105*x^3 + 55*x^4 - 3*x^5 - 6*x^6 - 4*x^7 + 6*x^8 - 2*x^9) / (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>10.

%F (End)

%e Some solutions for n=3:

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

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

%Y Cf. A220044.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 03 2012

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Last modified December 1 05:02 EST 2022. Contains 358454 sequences. (Running on oeis4.)