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A220036 Number of 6 X n arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..1 6 X n array. 1

%I

%S 7,12,28,83,187,358,613,962,1426,2034,2823,3839,5137,6782,8850,11429,

%T 14620,18538,23313,29091,36035,44326,54164,65769,79382,95266,113707,

%U 135015,159525,187598,219622,256013,297216,343706,395989,454603,520119

%N Number of 6 X n arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..1 6 X n array.

%C Row 6 of A220032.

%H R. H. Hardin, <a href="/A220036/b220036.txt">Table of n, a(n) for n = 1..155</a>

%F Empirical: a(n) = (1/120)*n^5 - (1/12)*n^4 + (47/24)*n^3 - (23/12)*n^2 + (1771/30)*n - 323 for n>8.

%F Conjectures from _Colin Barker_, Jul 30 2018: (Start)

%F G.f.: x*(7 - 30*x + 61*x^2 - 45*x^3 - 26*x^4 + 59*x^5 - 35*x^6 + 3*x^7 + 24*x^8 - 21*x^9 + 3*x^10 + x^11 - x^12 + x^13) / (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>14.

%F (End)

%e Some solutions for n=3:

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

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

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

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

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

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

%Y Cf. A220032.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 03 2012

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Last modified January 27 15:45 EST 2022. Contains 350607 sequences. (Running on oeis4.)