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A224150 Number of 6 X n 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.

%I A224150 #8 Aug 28 2018 09:45:56
%S A224150 7,49,242,930,2985,8375,21183,49365,107697,222603,439909,837071,
%T A224150 1542126,2762572,4828665,8257309,13844903,22800305,36932600,58912756,
%U A224150 92633675,143699769,220085207,333009601,498091361,736852507,1078664659,1563244537
%N A224150 Number of 6 X n 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.
%C A224150 Row 6 of A224146.
%H A224150 R. H. Hardin, <a href="/A224150/b224150.txt">Table of n, a(n) for n = 1..210</a>
%F A224150 Empirical: a(n) = (1/479001600)*n^12 + (1/26611200)*n^11 + (43/43545600)*n^10 + (29/1451520)*n^9 + (5671/14515200)*n^8 + (2219/345600)*n^7 + (2174569/43545600)*n^6 + (116341/483840)*n^5 + (8531549/10886400)*n^4 + (2862857/1814400)*n^3 + (3602461/1663200)*n^2 + (2327/1980)*n + 1.
%F A224150 Conjectures from _Colin Barker_, Aug 28 2018: (Start)
%F A224150 G.f.: x*(7 - 42*x + 151*x^2 - 396*x^3 + 762*x^4 - 1076*x^5 + 1137*x^6 - 906*x^7 + 538*x^8 - 230*x^9 + 67*x^10 - 12*x^11 + x^12) / (1 - x)^13.
%F A224150 a(n) = 13*a(n-1) - 78*a(n-2) + 286*a(n-3) - 715*a(n-4) + 1287*a(n-5) - 1716*a(n-6) + 1716*a(n-7) - 1287*a(n-8) + 715*a(n-9) - 286*a(n-10) + 78*a(n-11) - 13*a(n-12) + a(n-13) for n>13.
%F A224150 (End)
%e A224150 Some solutions for n=3:
%e A224150 ..0..0..0....0..0..0....0..1..0....0..0..0....1..0..0....0..0..0....0..0..1
%e A224150 ..0..0..0....0..0..0....1..1..0....0..0..0....1..0..0....0..0..0....0..0..1
%e A224150 ..1..1..0....0..0..1....1..1..0....0..1..0....1..0..0....1..0..0....0..0..1
%e A224150 ..1..1..0....0..1..1....1..1..0....0..1..0....1..1..1....1..0..0....0..0..1
%e A224150 ..1..1..0....0..1..1....1..1..1....0..1..0....1..1..1....1..1..0....0..1..1
%e A224150 ..1..1..1....0..1..1....1..1..1....1..1..0....1..1..1....1..1..0....1..1..1
%Y A224150 Cf. A224146.
%K A224150 nonn
%O A224150 1,1
%A A224150 _R. H. Hardin_, Mar 31 2013