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A224144 Number of n X 6 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.

%I A224144 #8 Aug 28 2018 05:50:51
%S A224144 22,148,554,1573,3827,8375,16885,31841,56783,96579,157729,248701,
%T A224144 380299,566063,822701,1170553,1634087,2242427,3029913,4036693,5309347,
%U A224144 6901543,8874725,11298833,14253055,17826611,22119569,27243693,33323323,40496287
%N A224144 Number of n X 6 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.
%C A224144 Column 6 of A224146.
%H A224144 R. H. Hardin, <a href="/A224144/b224144.txt">Table of n, a(n) for n = 1..210</a>
%F A224144 Empirical: a(n) = (2/45)*n^6 + (4/15)*n^5 + (16/9)*n^4 + 6*n^3 + (683/45)*n^2 + (341/15)*n - 55 for n>3.
%F A224144 Conjectures from _Colin Barker_, Aug 28 2018: (Start)
%F A224144 G.f.: x*(22 - 6*x - 20*x^2 + 33*x^3 + 40*x^4 - 53*x^5 + 8*x^6 + 11*x^7 - 2*x^8 - x^9) / (1 - x)^7.
%F A224144 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>10.
%F A224144 (End)
%e A224144 Some solutions for n=3:
%e A224144 ..0..1..0..0..0..0....0..0..0..1..0..0....0..0..0..1..0..0....1..0..0..0..0..0
%e A224144 ..0..1..0..0..0..0....0..0..1..1..1..0....0..0..1..1..0..0....1..1..1..1..0..0
%e A224144 ..0..1..1..0..0..0....0..0..1..1..1..0....1..1..1..1..1..1....1..1..1..1..1..0
%Y A224144 Cf. A224146.
%K A224144 nonn
%O A224144 1,1
%A A224144 _R. H. Hardin_, Mar 31 2013