login
Number of 2 X n arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 2 X n array.
1

%I #7 Jul 28 2018 12:16:04

%S 6,7,17,33,56,86,125,173,230,296,371,455,548,650,761,881,1010,1148,

%T 1295,1451,1616,1790,1973,2165,2366,2576,2795,3023,3260,3506,3761,

%U 4025,4298,4580,4871,5171,5480,5798,6125,6461,6806,7160,7523,7895,8276,8666,9065

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

%C Row 2 of A219852.

%H R. H. Hardin, <a href="/A219853/b219853.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (9/2)*n^2 - (39/2)*n + 41 for n>4.

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

%F G.f.: x*(6 - 11*x + 14*x^2 - 3*x^3 + x^4 + 2*x^6) / (1 - x)^3.

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>5.

%F (End)

%e Some solutions for n=3:

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

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

%Y Cf. A219852.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 29 2012