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A224149 Number of 5 X n 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.

%I A224149 #8 Aug 28 2018 07:08:10
%S A224149 6,36,155,526,1509,3827,8838,18969,38392,74053,137204,245636,426869,
%T A224149 722624,1194983,1934737,3072530,4793530,7356497,11118274,16564901,
%U A224149 24350745,35347252,50703161,71918276,100933171,140237506,192999960
%N A224149 Number of 5 X n 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.
%C A224149 Row 5 of A224146.
%H A224149 R. H. Hardin, <a href="/A224149/b224149.txt">Table of n, a(n) for n = 1..210</a>
%F A224149 Empirical: a(n) = (1/3628800)*n^10 + (1/241920)*n^9 + (11/120960)*n^8 + (59/40320)*n^7 + (3853/172800)*n^6 + (181/1280)*n^5 + (100381/181440)*n^4 + (76319/60480)*n^3 + (24247/12600)*n^2 + (23/21)*n + 1.
%F A224149 Conjectures from _Colin Barker_, Aug 28 2018: (Start)
%F A224149 G.f.: x*(6 - 30*x + 89*x^2 - 189*x^3 + 288*x^4 - 309*x^5 + 236*x^6 - 127*x^7 + 46*x^8 - 10*x^9 + x^10) / (1 - x)^11.
%F A224149 a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11) for n>11.
%F A224149 (End)
%e A224149 Some solutions for n=3:
%e A224149 ..0..1..0....0..0..0....0..1..0....0..0..0....0..0..0....0..0..1....0..0..0
%e A224149 ..1..1..0....0..0..0....0..1..0....0..1..0....0..1..0....0..0..1....1..0..0
%e A224149 ..1..1..1....0..1..0....0..1..0....0..1..1....1..1..0....0..1..1....1..1..0
%e A224149 ..1..1..1....0..1..0....0..1..0....1..1..1....1..1..0....0..1..1....1..1..0
%e A224149 ..1..1..1....1..1..1....1..1..1....1..1..1....1..1..1....0..1..1....1..1..1
%Y A224149 Cf. A224146.
%K A224149 nonn
%O A224149 1,1
%A A224149 _R. H. Hardin_, Mar 31 2013