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A224159 Number of 3 X n 0..1 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

%I A224159 #8 Aug 28 2018 15:02:04
%S A224159 8,36,89,187,373,702,1252,2130,3479,5486,8391,12497,18181,25906,36234,
%T A224159 49840,67527,90242,119093,155367,200549,256342,324688,407790,508135,
%U A224159 628518,772067,942269,1142997,1378538,1653622,1973452,2343735,2770714
%N A224159 Number of 3 X n 0..1 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.
%C A224159 Row 3 of A224158.
%H A224159 R. H. Hardin, <a href="/A224159/b224159.txt">Table of n, a(n) for n = 1..210</a>
%F A224159 Empirical: a(n) = (1/720)*n^6 + (1/240)*n^5 + (47/144)*n^4 - (3/16)*n^3 + (1111/180)*n^2 - (199/60)*n + 20 for n>2.
%F A224159 Conjectures from _Colin Barker_, Aug 28 2018: (Start)
%F A224159 G.f.: x*(8 - 20*x + 5*x^2 + 40*x^3 - 47*x^4 - 5*x^5 + 41*x^6 - 27*x^7 + 6*x^8) / (1 - x)^7.
%F A224159 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>9.
%F A224159 (End)
%e A224159 Some solutions for n=3:
%e A224159 ..0..0..1....0..0..1....0..0..0....0..1..0....1..0..0....0..1..1....1..1..0
%e A224159 ..1..1..0....1..1..0....0..0..0....1..0..0....0..1..0....1..1..1....1..0..0
%e A224159 ..1..1..1....1..1..0....1..0..0....0..1..0....1..0..0....1..1..0....1..1..0
%Y A224159 Cf. A224158.
%K A224159 nonn
%O A224159 1,1
%A A224159 _R. H. Hardin_, Mar 31 2013