A219846 - OEIS

%I #8 Jul 28 2018 10:43:39

%S 3,7,16,33,62,108,177,276,413,597,838,1147,1536,2018,2607,3318,4167,

%T 5171,6348,7717,9298,11112,13181,15528,18177,21153,24482,28191,32308,

%U 36862,41883,47402,53451,60063,67272,75113,83622,92836,102793,113532,125093

%N Number of n X 2 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 n X 2 array.

%C Column 2 of A219852.

%H R. H. Hardin, <a href="/A219846/b219846.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/24)*n^4 + (1/12)*n^3 + (23/24)*n^2 - (1/12)*n + 2.

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

%F G.f.: x*(3 - 8*x + 11*x^2 - 7*x^3 + 2*x^4) / (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>5.

%F (End)

%e Some solutions for n=3:

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

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

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

%Y Cf. A219852.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 29 2012