%I #7 Sep 05 2018 06:13:32

%S 29,239,1163,4166,12174,30738,69498,144111,278707,508937,885677,

%T 1479452,2385644,3730548,5678340,8439021,12277401,17523187,24582239,

%U 33949058,46220570,62111270,82469790,108296955,140765391,181240749,231304609

%N Number of n X 7 0..1 arrays with rows unimodal and columns nondecreasing.

%H R. H. Hardin, <a href="/A225009/b225009.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (4/315)*n^7 + (1/5)*n^6 + (58/45)*n^5 + (35/8)*n^4 + (1507/180)*n^3 + (357/40)*n^2 + (2027/420)*n + 1.

%F Conjectures from _Colin Barker_, Sep 05 2018: (Start)

%F G.f.: x*(29 + 7*x + 63*x^2 - 70*x^3 + 56*x^4 - 28*x^5 + 8*x^6 - x^7) / (1 - x)^8.

%F a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.

%F (End)

%e Some solutions for n=3:

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

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

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

%Y Column 7 of A225010.

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 23 2013