%I #8 Aug 25 2018 16:15:40

%S 9,31,76,155,281,469,736,1101,1585,2211,3004,3991,5201,6665,8416,

%T 10489,12921,15751,19020,22771,27049,31901,37376,43525,50401,58059,

%U 66556,75951,86305,97681,110144,123761,138601,154735,172236,191179,211641,233701

%N Number of 2 X n 0..2 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

%C Row 2 of A223999.

%H R. H. Hardin, <a href="/A224000/b224000.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/12)*n^4 + 1*n^3 + (41/12)*n^2 + (7/2)*n + 1.

%F Conjectures from _Colin Barker_, Aug 25 2018: (Start)

%F G.f.: x*(9 - 14*x + 11*x^2 - 5*x^3 + 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..2....0..0..1....1..1..1....0..1..1....1..1..1....0..0..2....1..1..2

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

%Y Cf. A223999.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 30 2013