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A223640 Number of n X 4 0..1 arrays with rows, columns, diagonals and antidiagonals unimodal.

%I A223640 #8 Aug 22 2018 06:25:22
%S A223640 11,121,726,2962,9808,28450,74599,179991,404599,855417,1714062,
%T A223640 3275798,6002946,10596004,18086161,29953249,48273537,75902131,
%U A223640 116695104,175776840,259858436,377613366,540116971,761356699,1058820379,1454170173
%N A223640 Number of n X 4 0..1 arrays with rows, columns, diagonals and antidiagonals unimodal.
%C A223640 Column 4 of A223644.
%H A223640 R. H. Hardin, <a href="/A223640/b223640.txt">Table of n, a(n) for n = 1..210</a>
%F A223640 Empirical: a(n) = (1/112)*n^8 - (19/210)*n^7 + (107/90)*n^6 - (197/40)*n^5 + (2219/144)*n^4 + (5093/120)*n^3 - (868411/2520)*n^2 + (417721/420)*n - 1091 for n>4.
%F A223640 Conjectures from _Colin Barker_, Aug 22 2018: (Start)
%F A223640 G.f.: x*(11 + 22*x + 33*x^2 - 140*x^3 + 508*x^4 - 314*x^5 - 17*x^6 + 432*x^7 - 233*x^8 + 28*x^9 + 56*x^10 - 28*x^11 + 2*x^12) / (1 - x)^9.
%F A223640 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 A223640 (End)
%e A223640 Some solutions for n=4:
%e A223640 ..0..1..0..0....1..1..0..0....1..0..0..0....0..1..1..1....0..0..1..1
%e A223640 ..0..1..1..1....1..1..1..0....0..1..0..0....0..0..1..1....0..1..1..1
%e A223640 ..0..1..1..0....0..1..1..1....0..0..0..0....0..0..0..0....0..0..0..0
%e A223640 ..0..0..1..0....0..0..0..1....0..0..1..0....0..0..0..0....0..0..0..0
%Y A223640 Cf. A223644.
%K A223640 nonn
%O A223640 1,1
%A A223640 _R. H. Hardin_, Mar 24 2013