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A223632 Number of n X 3 0..1 arrays with rows, antidiagonals and columns unimodal.

%I A223632 #8 Aug 22 2018 02:02:02
%S A223632 7,49,229,801,2297,5699,12657,25753,48811,87253,148501,242425,381837,
%T A223632 583031,866369,1256913,1785103,2487481,3407461,4596145,6113185,
%U A223632 8027691,10419185,13378601,17009331,21428317,26767189,33173449,40811701,49864927
%N A223632 Number of n X 3 0..1 arrays with rows, antidiagonals and columns unimodal.
%C A223632 Column 3 of A223637.
%H A223632 R. H. Hardin, <a href="/A223632/b223632.txt">Table of n, a(n) for n = 1..210</a>
%F A223632 Empirical: a(n) = (23/360)*n^6 + (11/120)*n^5 + (91/72)*n^4 + (11/8)*n^3 + (301/180)*n^2 + (23/15)*n + 1.
%F A223632 Conjectures from _Colin Barker_, Aug 21 2018: (Start)
%F A223632 G.f.: x*(7 + 33*x^2 - 18*x^3 + 29*x^4 - 6*x^5 + x^6) / (1 - x)^7.
%F A223632 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 A223632 (End)
%e A223632 Some solutions for n=4:
%e A223632 ..0..0..1....1..1..0....0..0..0....1..1..0....0..1..0....0..1..0....1..1..0
%e A223632 ..1..0..0....0..1..1....0..0..0....1..1..0....1..1..0....0..1..1....0..1..0
%e A223632 ..0..1..0....0..1..0....1..0..0....1..1..0....0..0..1....1..1..1....0..0..0
%e A223632 ..0..1..0....0..1..0....1..1..1....1..1..0....0..0..1....1..1..0....0..0..0
%Y A223632 Cf. A223637.
%K A223632 nonn
%O A223632 1,1
%A A223632 _R. H. Hardin_, Mar 24 2013