login
Number of n X 2 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 columns, 0..2 n X 2 array.
2

%I #8 Mar 11 2018 10:09:09

%S 3,3,7,12,21,35,57,91,142,216,320,462,651,897,1211,1605,2092,2686,

%T 3402,4256,5265,6447,7821,9407,11226,13300,15652,18306,21287,24621,

%U 28335,32457,37016,42042,47566,53620,60237,67451,75297,83811,93030,102992

%N Number of n X 2 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 columns, 0..2 n X 2 array.

%C Column 2 of A219217.

%H R. H. Hardin, <a href="/A219211/b219211.txt">Table of n, a(n) for n = 1..185</a>

%F Empirical: a(n) = (1/24)*n^4 - (5/12)*n^3 + (59/24)*n^2 - (37/12)*n + 1 for n>3.

%F Conjectures from _Colin Barker_, Mar 11 2018: (Start)

%F G.f.: x*(3 - 12*x + 22*x^2 - 23*x^3 + 16*x^4 - 8*x^5 + 4*x^6 - x^7) / (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 All solutions for n=3:

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

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

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

%Y Cf. A219217.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 14 2012