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A219472 Number of 2 X n arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..3 2 X n array. 1

%I

%S 10,23,68,211,547,1248,2663,5432,10666,20206,36984,65512,112528,

%T 187831,305340,484415,751481,1141999,1702831,2495049,3597241,5109370,

%U 7157245,9897666,13524308,18274412,24436354,32358166,42457086,55230217,71266378

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

%C Row 2 of A219471.

%H R. H. Hardin, <a href="/A219472/b219472.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/13440)*n^8 + (1/10080)*n^7 + (1/576)*n^6 + (119/720)*n^5 - (9659/5760)*n^4 + (18247/1440)*n^3 - (50047/2016)*n^2 + (6437/840)*n + 13 for n>3.

%F Conjectures from _Colin Barker_, Jul 26 2018: (Start)

%F G.f.: x*(10 - 67*x + 221*x^2 - 413*x^3 + 424*x^4 - 153*x^5 - 91*x^6 + 35*x^7 + 124*x^8 - 129*x^9 + 49*x^10 - 7*x^11) / (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>12.

%F (End)

%e Some solutions for n=3:

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

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

%Y Cf. A219471.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 20 2012

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Last modified October 21 06:58 EDT 2021. Contains 348145 sequences. (Running on oeis4.)