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A224142 Number of n X 4 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.

%I A224142 #7 Aug 27 2018 16:47:25
%S A224142 11,46,124,272,526,930,1536,2404,3602,5206,7300,9976,13334,17482,
%T A224142 22536,28620,35866,44414,54412,66016,79390,94706,112144,131892,154146,
%U A224142 179110,206996,238024,272422,310426,352280,398236,448554,503502,563356,628400
%N A224142 Number of n X 4 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.
%C A224142 Column 4 of A224146.
%H A224142 R. H. Hardin, <a href="/A224142/b224142.txt">Table of n, a(n) for n = 1..210</a>
%F A224142 Empirical: a(n) = (1/3)*n^4 + (4/3)*n^3 + (14/3)*n^2 + (23/3)*n - 4 for n>1.
%F A224142 Conjectures from _Colin Barker_, Aug 27 2018: (Start)
%F A224142 G.f.: x*(11 - 9*x + 4*x^2 + 2*x^3 + x^4 - x^5) / (1 - x)^5.
%F A224142 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>6.
%F A224142 (End)
%e A224142 Some solutions for n=3:
%e A224142 ..0..1..0..0....0..0..0..0....0..0..0..0....0..0..1..0....1..1..1..0
%e A224142 ..0..1..1..0....0..1..0..0....1..1..1..0....0..0..1..1....1..1..1..1
%e A224142 ..0..1..1..0....1..1..0..0....1..1..1..1....0..1..1..1....1..1..1..1
%Y A224142 Cf. A224146.
%K A224142 nonn
%O A224142 1,1
%A A224142 _R. H. Hardin_, Mar 31 2013