%I #7 Aug 27 2018 16:19:23

%S 7,22,49,92,155,242,357,504,687,910,1177,1492,1859,2282,2765,3312,

%T 3927,4614,5377,6220,7147,8162,9269,10472,11775,13182,14697,16324,

%U 18067,19930,21917,24032,26279,28662,31185,33852,36667,39634,42757,46040,49487,53102

%N Number of n X 3 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.

%C Column 3 of A224146.

%H R. H. Hardin, <a href="/A224141/b224141.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (2/3)*n^3 + 2*n^2 + (13/3)*n.

%F Conjectures from _Colin Barker_, Aug 27 2018: (Start)

%F G.f.: x*(7 - 6*x + 3*x^2) / (1 - x)^4.

%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.

%F (End)

%e Some solutions for n=3:

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

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

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

%Y Cf. A224146.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 31 2013