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A223772 Number of n X 3 0..1 arrays with rows and columns unimodal and antidiagonals nondecreasing.

%I A223772 #7 Aug 23 2018 08:29:43
%S A223772 7,28,78,180,371,707,1269,2170,3563,5650,8692,13020,19047,27281,38339,
%T A223772 52962,72031,96584,127834,167188,216267,276927,351281,441722,550947,
%U A223772 681982,838208,1023388,1241695,1497741,1796607,2143874,2545655,3008628
%N A223772 Number of n X 3 0..1 arrays with rows and columns unimodal and antidiagonals nondecreasing.
%C A223772 Column 3 of A223777.
%H A223772 R. H. Hardin, <a href="/A223772/b223772.txt">Table of n, a(n) for n = 1..210</a>
%F A223772 Empirical: a(n) = (1/720)*n^6 + (1/80)*n^5 + (29/144)*n^4 + (25/48)*n^3 + (1727/360)*n^2 - (8/15)*n + 2.
%F A223772 Conjectures from _Colin Barker_, Aug 23 2018: (Start)
%F A223772 G.f.: x*(7 - 21*x + 29*x^2 - 23*x^3 + 14*x^4 - 7*x^5 + 2*x^6) / (1 - x)^7.
%F A223772 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 A223772 (End)
%e A223772 Some solutions for n=3:
%e A223772 ..0..1..1....1..0..0....1..1..1....1..0..0....1..0..0....0..0..0....0..1..0
%e A223772 ..1..1..0....1..0..0....1..1..1....1..0..0....1..0..0....0..1..0....1..1..0
%e A223772 ..1..0..0....0..0..0....1..1..1....1..1..0....1..1..1....1..1..1....1..0..0
%Y A223772 Cf. A223777.
%K A223772 nonn
%O A223772 1,1
%A A223772 _R. H. Hardin_, Mar 27 2013