A219803 - OEIS

A219803

Number of 2 X n arrays of the minimum value of corresponding elements and their horizontal, vertical, diagonal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..3 2 X n array.

%I #8 Jul 28 2018 10:43:21

%S 4,4,10,21,39,68,114,186,297,465,714,1075,1587,2298,3266,4560,6261,

%T 8463,11274,14817,19231,24672,31314,39350,48993,60477,74058,90015,

%U 108651,130294,155298,184044,216941,254427,296970,345069,399255,460092,528178

%N Number of 2 X n arrays of the minimum value of corresponding elements and their horizontal, vertical, diagonal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..3 2 X n array.

%C Row 2 of A219802.

%H R. H. Hardin, <a href="/A219803/b219803.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/120)*n^5 - (1/8)*n^4 + (29/24)*n^3 - (35/8)*n^2 + (737/60)*n - 12 for n>2.

%F Conjectures from _Colin Barker_, Jul 28 2018: (Start)

%F G.f.: x*(4 - 20*x + 46*x^2 - 59*x^3 + 43*x^4 - 15*x^5 + x^6 + x^7) / (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>8.

%F (End)

%e Some solutions for n=3:

%e ..3..3..3....1..0..0....2..0..0....2..2..2....2..1..1....3..0..0....0..0..0

%Y Cf. A219802.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 28 2012