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 A219715 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 nonincreasing columns, 0..3 2 X n array. 1

%I

%S 10,13,45,125,283,561,1030,1776,2916,4610,7073,10587,15513,22303,

%T 31512,43810,59994,81000,107915,141989,184647,237501,302362,381252,

%U 476416,590334,725733,885599,1073189,1292043,1545996,1839190,2176086,2561476

%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 nonincreasing columns, 0..3 2 X n array.

%C Row 2 of A219714.

%H R. H. Hardin, <a href="/A219715/b219715.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/10)*n^5 - (53/24)*n^4 + (117/4)*n^3 - (4099/24)*n^2 + (10233/20)*n - 594 for n>4.

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

%F G.f.: x*(10 - 47*x + 117*x^2 - 150*x^3 + 98*x^4 - 27*x^5 + 16*x^6 - 31*x^7 + 30*x^8 - 4*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..1..1....0..0..0....2..0..0....2..2..1....2..1..1....2..0..0....2..0..0

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

%Y Cf. A219714.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 26 2012

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Last modified November 27 09:16 EST 2022. Contains 358367 sequences. (Running on oeis4.)