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%I #8 Aug 26 2018 11:11:44
%S 32,144,298,488,734,1064,1505,2091,2864,3875,5185,6866,9002,11690,
%T 15041,19181,24252,30413,37841,46732,57302,69788,84449,101567,121448,
%U 144423,170849,201110,235618,274814,319169,369185,425396,488369,558705,637040
%N Number of 5 X n 0..1 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.
%C Row 5 of A224038.
%H R. H. Hardin, <a href="/A224041/b224041.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/120)*n^5 + (1/24)*n^4 + (25/24)*n^3 + (227/24)*n^2 + (1289/20)*n - 7 for n>3.
%F Conjectures from _Colin Barker_, Aug 26 2018: (Start)
%F G.f.: x*(32 - 48*x - 86*x^2 + 220*x^3 - 124*x^4 - 12*x^5 + 9*x^6 + 17*x^7 - 7*x^8) / (1 - x)^6.
%F a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>9.
%F (End)
%e Some solutions for n=3:
%e ..0..0..1....0..0..0....1..1..1....0..0..1....1..1..1....0..0..0....0..1..1
%e ..0..0..0....0..0..0....0..1..1....0..0..0....1..1..1....0..0..1....0..1..1
%e ..0..0..1....0..1..1....0..1..1....0..0..0....0..1..1....0..0..1....0..1..1
%e ..0..1..1....1..1..1....0..1..1....0..0..0....1..1..1....0..0..0....0..1..1
%e ..0..0..1....1..1..1....0..1..1....0..1..1....0..1..1....0..1..1....1..1..1
%Y Cf. A224038.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 30 2013
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