A219699 - OEIS

%I #8 Jul 27 2018 06:11:48

%S 3,5,13,25,45,78,130,208,320,475,683,955,1303,1740,2280,2938,3730,

%T 4673,5785,7085,8593,10330,12318,14580,17140,20023,23255,26863,30875,

%U 35320,40228,45630,51558,58045,65125,72833,81205,90278,100090,110680,122088

%N Number of n X 3 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 3 array.

%C Column 3 of A219704.

%H R. H. Hardin, <a href="/A219699/b219699.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/24)*n^4 + (1/12)*n^3 - (25/24)*n^2 + (107/12)*n - 10 for n>1.

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

%F G.f.: x*(3 - 10*x + 18*x^2 - 20*x^3 + 15*x^4 - 5*x^5) / (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>6.

%F (End)

%e Some solutions for n=3:

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

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

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

%Y Cf. A219704.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 25 2012