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A219293 Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal, vertical or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..2 n X 2 array. 1

%I

%S 3,7,17,35,62,103,165,257,390,577,833,1175,1622,2195,2917,3813,4910,

%T 6237,7825,9707,11918,14495,17477,20905,24822,29273,34305,39967,46310,

%U 53387,61253,69965,79582,90165,101777,114483,128350,143447,159845,177617

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

%C Column 2 of A219299.

%H R. H. Hardin, <a href="/A219293/b219293.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/12)*n^4 - (2/3)*n^3 + (53/12)*n^2 - (17/6)*n - 3 for n > 2.

%F Conjectures from _Colin Barker_, Jul 25 2018: (Start)

%F G.f.: x*(3 - 8*x + 12*x^2 - 10*x^3 + 2*x^4 + 5*x^5 - 2*x^6) / (1 - x)^5.

%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n > 7.

%F (End)

%e Some solutions for n=3:

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

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

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

%Y Cf. A219299.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 17 2012

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Last modified September 28 22:34 EDT 2021. Contains 347717 sequences. (Running on oeis4.)