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A219708 Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..3 n X 2 array. 1

%I

%S 4,13,44,129,338,813,1822,3840,7665,14578,26557,46556,78861,129536,

%T 206973,322561,491490,733707,1075042,1548523,2195900,3069399,4233728,

%U 5768358,7770103,10356024,13666683,17869774,23164159,29784338,38005383

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

%C Column 2 of A219714.

%H R. H. Hardin, <a href="/A219708/b219708.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/40320)*n^8 + (1/2016)*n^7 + (7/2880)*n^6 + (5/144)*n^5 + (167/5760)*n^4 + (259/288)*n^3 + (4723/10080)*n^2 - (73/168)*n + 3.

%F Conjectures from _Colin Barker_, Jul 27 2018: (Start)

%F G.f.: x*(4 - 23*x + 71*x^2 - 135*x^3 + 173*x^4 - 147*x^5 + 79*x^6 - 24*x^7 + 3*x^8) / (1 - x)^9.

%F a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.

%F (End)

%e Some solutions for n=3:

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

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

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

%Y Cf. A219714.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 26 2012

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Last modified September 25 23:58 EDT 2021. Contains 347664 sequences. (Running on oeis4.)