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A224014 Number of 4 X n 0..2 arrays with rows nondecreasing and antidiagonals unimodal.

%I A224014 #8 Aug 26 2018 06:30:04
%S A224014 81,1296,7378,28541,90051,245055,595822,1325316,2742301,5343468,
%T A224014 9896484,17548273,29963249,49496631,79408380,124123708,189546519,
%U A224014 283432552,415829406,599591037,850974727,1190328935,1642880850,2239632876
%N A224014 Number of 4 X n 0..2 arrays with rows nondecreasing and antidiagonals unimodal.
%C A224014 Row 4 of A224012.
%H A224014 R. H. Hardin, <a href="/A224014/b224014.txt">Table of n, a(n) for n = 1..210</a>
%F A224014 Empirical: a(n) = (41/4032)*n^8 + (55/336)*n^7 + (733/480)*n^6 + (1037/120)*n^5 + (4789/192)*n^4 + (2125/48)*n^3 + (216821/5040)*n^2 + (9329/210)*n + 4 for n>2.
%F A224014 Conjectures from _Colin Barker_, Aug 26 2018: (Start)
%F A224014 G.f.: x*(81 + 567*x - 1370*x^2 + 1991*x^3 + 132*x^4 - 4590*x^5 + 7855*x^6 - 6900*x^7 + 3514*x^8 - 990*x^9 + 120*x^10) / (1 - x)^9.
%F A224014 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 A224014 (End)
%e A224014 Some solutions for n=3:
%e A224014 ..0..1..2....1..1..2....1..2..2....0..2..2....1..2..2....2..2..2....1..1..1
%e A224014 ..0..1..2....0..0..0....1..1..2....0..1..2....1..2..2....1..1..1....1..1..1
%e A224014 ..0..2..2....0..0..2....1..1..1....0..2..2....1..1..1....1..1..1....0..2..2
%e A224014 ..0..0..1....0..1..2....0..1..2....1..1..2....0..0..2....1..1..1....2..2..2
%Y A224014 Cf. A224012.
%K A224014 nonn
%O A224014 1,1
%A A224014 _R. H. Hardin_, Mar 30 2013