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A225009 Number of n X 7 0..1 arrays with rows unimodal and columns nondecreasing.

%I A225009 #7 Sep 05 2018 06:13:32
%S A225009 29,239,1163,4166,12174,30738,69498,144111,278707,508937,885677,
%T A225009 1479452,2385644,3730548,5678340,8439021,12277401,17523187,24582239,
%U A225009 33949058,46220570,62111270,82469790,108296955,140765391,181240749,231304609
%N A225009 Number of n X 7 0..1 arrays with rows unimodal and columns nondecreasing.
%H A225009 R. H. Hardin, <a href="/A225009/b225009.txt">Table of n, a(n) for n = 1..210</a>
%F A225009 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 A225009 Conjectures from _Colin Barker_, Sep 05 2018: (Start)
%F A225009 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 A225009 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 A225009 (End)
%e A225009 Some solutions for n=3:
%e A225009 ..0..1..1..0..0..0..0....1..1..1..1..0..0..0....0..0..0..0..0..0..0
%e A225009 ..0..1..1..1..1..0..0....1..1..1..1..1..0..0....1..1..0..0..0..0..0
%e A225009 ..1..1..1..1..1..1..1....1..1..1..1..1..1..1....1..1..0..0..0..0..0
%Y A225009 Column 7 of A225010.
%K A225009 nonn
%O A225009 1,1
%A A225009 _R. H. Hardin_, Apr 23 2013