%I #7 Aug 23 2018 08:29:33

%S 11,56,180,461,1040,2164,4246,7950,14308,24877,41945,68796,110045,

%T 172055,263449,395731,584031,847990,1212802,1710431,2381022,3274526,

%U 4452560,5990524,7979998,10531443,13777231,17875030,23011571,29406825,37318619

%N Number of n X 4 0..1 arrays with rows and columns unimodal and antidiagonals nondecreasing.

%C Column 4 of A223777.

%H R. H. Hardin, <a href="/A223773/b223773.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/40320)*n^8 + (1/3360)*n^7 + (19/2880)*n^6 + (7/120)*n^5 + (2447/5760)*n^4 + (259/160)*n^3 + (126691/10080)*n^2 - (12329/840)*n + 13 for n>1.

%F Conjectures from _Colin Barker_, Aug 23 2018: (Start)

%F G.f.: x*(11 - 43*x + 72*x^2 - 67*x^3 + 53*x^4 - 50*x^5 + 34*x^6 - 6*x^7 - 5*x^8 + 2*x^9) / (1 - x)^9.

%F a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>10.

%F (End)

%e Some solutions for n=3:

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

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

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

%Y Cf. A223777.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 27 2013