A220033 - OEIS

%I #7 Jul 30 2018 06:14:14

%S 4,6,10,19,30,42,55,69,84,100,117,135,154,174,195,217,240,264,289,315,

%T 342,370,399,429,460,492,525,559,594,630,667,705,744,784,825,867,910,

%U 954,999,1045,1092,1140,1189,1239,1290,1342,1395,1449,1504,1560,1617,1675

%N Number of 3 X n arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..1 3 X n array.

%C Row 3 of A220032.

%H R. H. Hardin, <a href="/A220033/b220033.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/2)*n^2 + (13/2)*n - 15 for n>3.

%F Conjectures from _Colin Barker_, Jul 30 2018: (Start)

%F G.f.: x*(4 - 6*x + 4*x^2 + 3*x^3 - 3*x^4 - x^5) / (1 - x)^3.

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>6.

%F (End)

%e Some solutions for n=3:

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

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

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

%Y Cf. A220032.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 03 2012