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A223615 Number of n X 3 0..1 arrays with rows and columns unimodal.

%I A223615 #8 Aug 21 2018 10:04:30
%S A223615 7,49,240,876,2582,6504,14547,29659,56161,100123,169786,276030,432888,
%T A223615 658106,973749,1406853,1990123,2762677,3770836,5068960,6720330,
%U A223615 8798076,11386151,14580351,18489381,23235967,28958014,35809810,43963276,53609262
%N A223615 Number of n X 3 0..1 arrays with rows and columns unimodal.
%C A223615 Column 3 of A223620.
%H A223615 R. H. Hardin, <a href="/A223615/b223615.txt">Table of n, a(n) for n = 1..210</a>
%F A223615 Empirical: a(n) = (23/360)*n^6 + (31/120)*n^5 + (8/9)*n^4 + (31/24)*n^3 + (737/360)*n^2 + (29/20)*n + 1.
%F A223615 Conjectures from _Colin Barker_, Aug 21 2018: (Start)
%F A223615 G.f.: x*(7 + 44*x^2 - 20*x^3 + 20*x^4 - 6*x^5 + x^6) / (1 - x)^7.
%F A223615 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 A223615 (End)
%e A223615 Some solutions for n=4:
%e A223615 ..0..0..1....0..0..1....1..0..0....0..0..1....0..1..0....0..0..0....0..1..1
%e A223615 ..0..1..1....0..1..1....1..1..1....0..0..1....0..1..1....1..0..0....0..1..0
%e A223615 ..1..1..1....0..0..1....1..1..0....0..1..0....0..0..1....1..0..0....0..0..0
%e A223615 ..1..1..1....0..0..1....0..1..0....0..1..0....0..0..0....1..1..0....1..0..0
%Y A223615 Cf. A223620.
%K A223615 nonn
%O A223615 1,1
%A A223615 _R. H. Hardin_, Mar 24 2013