A219500 - OEIS

%I #8 Jul 26 2018 06:35:10

%S 6,11,35,88,179,325,550,885,1369,2050,2986,4246,5911,8075,10846,14347,

%T 18717,24112,30706,38692,48283,59713,73238,89137,107713,129294,154234,

%U 182914,215743,253159,295630,343655,397765,458524,526530,602416,686851

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

%C Column 6 of A219502.

%H R. H. Hardin, <a href="/A219500/b219500.txt">Table of n, a(n) for n = 1..67</a>

%F Empirical: a(n) = (1/120)*n^5 + (1/24)*n^4 + (13/24)*n^3 + (59/24)*n^2 + (59/20)*n - 17 for n>3.

%F Conjectures from _Colin Barker_, Jul 26 2018: (Start)

%F G.f.: x*(6 - 25*x + 59*x^2 - 77*x^3 + 46*x^4 - 10*x^6 + x^7 + x^8) / (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>9.

%F (End)

%e Some solutions for n=3:

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

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

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

%Y Cf. A219502.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 20 2012