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A219774 Number of 3 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..1 3 X n array. 1

%I

%S 4,6,14,33,65,114,189,298,450,655,924,1269,1703,2240,2895,3684,4624,

%T 5733,7030,8535,10269,12254,14513,17070,19950,23179,26784,30793,35235,

%U 40140,45539,51464,57948,65025,72730,81099,90169,99978,110565,121970,134234

%N Number of 3 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..1 3 X n array.

%C Row 3 of A219773.

%H R. H. Hardin, <a href="/A219774/b219774.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/24)*n^4 + (1/4)*n^3 - (13/24)*n^2 + (17/4)*n for n>4.

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

%F G.f.: x*(4 - 14*x + 24*x^2 - 17*x^3 + 5*x^5 + 3*x^6 - 6*x^7 + 2*x^8) / (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>9.

%F (End)

%e Some solutions for n=3:

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

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

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

%Y Cf. A219773.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 27 2012

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Last modified August 11 19:26 EDT 2022. Contains 356066 sequences. (Running on oeis4.)