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A224160 Number of 4 X n 0..1 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.

%I A224160 #8 Aug 28 2018 15:36:58
%S A224160 16,108,281,574,1156,2271,4339,8008,14257,24519,40840,66082,104179,
%T A224160 160456,242022,358249,521350,747070,1055505,1472065,2028598,2764693,
%U A224160 3729181,4981854,6595423,8657737,11274286,14571012,18697453,23830246
%N A224160 Number of 4 X n 0..1 arrays with diagonals and rows unimodal and antidiagonals nondecreasing.
%C A224160 Row 4 of A224158.
%H A224160 R. H. Hardin, <a href="/A224160/b224160.txt">Table of n, a(n) for n = 1..210</a>
%F A224160 Empirical: a(n) = (1/40320)*n^8 - (1/10080)*n^7 + (31/2880)*n^6 + (43/720)*n^5 + (3527/5760)*n^4 - (5947/1440)*n^3 + (548119/10080)*n^2 - (119221/840)*n + 283 for n>4.
%F A224160 Conjectures from _Colin Barker_, Aug 28 2018: (Start)
%F A224160 G.f.: x*(16 - 36*x - 115*x^2 + 589*x^3 - 950*x^4 + 519*x^5 + 442*x^6 - 977*x^7 + 817*x^8 - 436*x^9 + 178*x^10 - 55*x^11 + 9*x^12) / (1 - x)^9.
%F A224160 a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>13.
%F A224160 (End)
%e A224160 Some solutions for n=3:
%e A224160 ..1..1..0....1..1..0....1..1..0....0..0..0....1..1..1....0..0..1....0..0..1
%e A224160 ..1..1..0....1..1..1....1..1..1....0..0..0....1..1..1....0..1..0....0..1..1
%e A224160 ..1..1..0....1..1..1....1..1..0....1..1..0....1..1..1....1..1..1....1..1..0
%e A224160 ..1..0..0....1..1..0....1..1..0....1..1..1....1..1..0....1..1..1....1..1..0
%Y A224160 Cf. A224158.
%K A224160 nonn
%O A224160 1,1
%A A224160 _R. H. Hardin_, Mar 31 2013