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A224411 Number of 4 X n 0..1 arrays with rows unimodal and antidiagonals nondecreasing.

%I A224411 #8 Aug 30 2018 19:37:32
%S A224411 16,108,358,884,1928,3902,7490,13784,24467,42053,70195,114073,180875,
%T A224411 280385,425693,634043,927836,1335806,1894388,2649298,3657346,4988504,
%U A224411 6728252,8980226,11869193,15544379,20183177,25995263,33227149,42167203
%N A224411 Number of 4 X n 0..1 arrays with rows unimodal and antidiagonals nondecreasing.
%C A224411 Row 4 of A224409.
%H A224411 R. H. Hardin, <a href="/A224411/b224411.txt">Table of n, a(n) for n = 1..210</a>
%F A224411 Empirical: a(n) = (1/40320)*n^8 + (1/1440)*n^7 + (31/2880)*n^6 + (13/144)*n^5 + (3767/5760)*n^4 + (6409/1440)*n^3 + (189859/10080)*n^2 - (73/24)*n - 7 for n>2.
%F A224411 Conjectures from _Colin Barker_, Aug 30 2018: (Start)
%F A224411 G.f.: x*(16 - 36*x - 38*x^2 + 206*x^3 - 196*x^4 - 106*x^5 + 368*x^6 - 334*x^7 + 155*x^8 - 38*x^9 + 4*x^10) / (1 - x)^9.
%F A224411 a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>11.
%F A224411 (End)
%e A224411 Some solutions for n=3:
%e A224411 ..0..0..0....0..0..0....0..0..0....1..0..0....0..0..0....1..1..0....0..0..0
%e A224411 ..0..0..1....0..0..0....1..1..0....0..1..1....1..1..0....1..1..0....1..0..0
%e A224411 ..0..1..0....1..1..1....1..1..1....1..1..1....1..0..0....1..1..0....0..1..0
%e A224411 ..1..0..0....1..1..1....1..1..1....1..1..0....0..1..0....1..0..0....1..0..0
%Y A224411 Cf. A224409.
%K A224411 nonn
%O A224411 1,1
%A A224411 _R. H. Hardin_, Apr 05 2013