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A219700 Number of n X 4 arrays of the minimum value of corresponding elements and their horizontal, vertical or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..1 n X 4 array. 1

%I

%S 4,7,25,64,158,374,841,1789,3619,7008,13059,23510,41018,69536,114803,

%T 184969,291379,449542,680313,1011318,1478654,2128898,3021461,4231325,

%U 5852203,8000164,10817767,14478750,19193322,25214108,32842799,42437561

%N Number of n X 4 arrays of the minimum value of corresponding elements and their horizontal, vertical or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..1 n X 4 array.

%C Column 4 of A219704.

%H R. H. Hardin, <a href="/A219700/b219700.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/20160)*n^8 - (1/1680)*n^7 + (1/160)*n^6 + (5/48)*n^5 - (2431/960)*n^4 + (1173/40)*n^3 - (874309/5040)*n^2 + (3728/7)*n - 647 for n>4.

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

%F G.f.: x*(4 - 29*x + 106*x^2 - 245*x^3 + 398*x^4 - 466*x^5 + 391*x^6 - 230*x^7 + 106*x^8 - 52*x^9 + 23*x^10 - 2*x^11 - 2*x^12) / (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>13.

%F (End)

%e Some solutions for n=3:

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

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

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

%Y Cf. A219704.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 25 2012

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Last modified December 1 02:46 EST 2021. Contains 349426 sequences. (Running on oeis4.)