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%I #7 Aug 24 2018 08:52:20
%S 64,729,2024,3645,5951,9919,16845,28558,47721,78071,124691,194314,
%T 295659,439799,640561,914958,1283653,1771455,2407847,3227546,4271095,
%U 5585487,7224821,9250990,11734401,14754727,18401691,22775882,27989603,34167751
%N Number of 6 X n 0..1 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.
%C Row 6 of A223949.
%H R. H. Hardin, <a href="/A223953/b223953.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (2/45)*n^6 + (67/36)*n^4 + 8*n^3 + (7757/180)*n^2 + 138*n + 1326 for n>4.
%F Conjectures from _Colin Barker_, Aug 24 2018: (Start)
%F G.f.: x*(64 + 281*x - 1735*x^2 + 2546*x^3 - 335*x^4 - 1862*x^5 + 787*x^6 + 767*x^7 - 426*x^8 - 148*x^9 + 93*x^10) / (1 - x)^7.
%F 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>11.
%F (End)
%e Some solutions for n=3:
%e ..0..1..1....0..0..0....1..1..1....1..1..1....0..0..1....1..1..1....0..0..1
%e ..0..0..0....0..0..0....0..1..1....0..1..1....0..1..1....0..0..1....0..0..1
%e ..0..0..0....0..0..1....1..1..1....0..0..0....0..0..0....0..0..0....0..0..0
%e ..0..0..0....0..0..1....1..1..1....0..0..0....0..0..0....0..0..1....0..1..1
%e ..0..1..1....0..1..1....0..0..1....0..1..1....0..0..1....0..0..1....1..1..1
%e ..0..0..0....0..0..1....0..0..0....0..0..1....1..1..1....0..0..1....0..0..0
%Y Cf. A223949.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 29 2013
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