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A225008 Number of n X 6 0..1 arrays with rows unimodal and columns nondecreasing.

%I A225008 #7 Sep 05 2018 05:59:46
%S A225008 22,148,610,1897,4900,11088,22716,43065,76714,129844,210574,329329,
%T A225008 499240,736576,1061208,1497105,2072862,2822260,3784858,5006617,
%U A225008 6540556,8447440,10796500,13666185,17144946,21332052,26338438,32287585,39316432
%N A225008 Number of n X 6 0..1 arrays with rows unimodal and columns nondecreasing.
%H A225008 R. H. Hardin, <a href="/A225008/b225008.txt">Table of n, a(n) for n = 1..210</a>
%F A225008 Empirical: a(n) = (2/45)*n^6 + (8/15)*n^5 + (91/36)*n^4 + 6*n^3 + (1337/180)*n^2 + (67/15)*n + 1.
%F A225008 Conjectures from _Colin Barker_, Sep 05 2018: (Start)
%F A225008 G.f.: x*(22 - 6*x + 36*x^2 - 35*x^3 + 21*x^4 - 7*x^5 + x^6) / (1 - x)^7.
%F A225008 a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
%F A225008 (End)
%e A225008 Some solutions for n=3:
%e A225008 ..0..1..0..0..0..0....0..0..1..0..0..0....0..0..1..1..1..0....0..0..1..1..0..0
%e A225008 ..0..1..0..0..0..0....0..1..1..1..1..0....0..0..1..1..1..0....0..1..1..1..1..0
%e A225008 ..0..1..1..1..0..0....1..1..1..1..1..0....0..1..1..1..1..1....0..1..1..1..1..0
%Y A225008 Column 6 of A225010.
%K A225008 nonn
%O A225008 1,1
%A A225008 _R. H. Hardin_, Apr 23 2013