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A224001 Number of 3 X n 0..2 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

%I A224001 #8 Aug 25 2018 15:35:14
%S A224001 27,157,476,1144,2403,4614,8291,14141,23109,36428,55674,82826,120331,
%T A224001 171174,238953,327959,443261,590796,777464,1011228,1301219,1657846,
%U A224001 2092911,2619729,3253253,4010204,4909206,5970926,7218219,8676278
%N A224001 Number of 3 X n 0..2 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.
%C A224001 Row 3 of A223999.
%H A224001 R. H. Hardin, <a href="/A224001/b224001.txt">Table of n, a(n) for n = 1..210</a>
%F A224001 Empirical: a(n) = (1/144)*n^6 + (5/48)*n^5 + (163/144)*n^4 + (85/16)*n^3 + (895/36)*n^2 - (65/12)*n + 3 for n>2.
%F A224001 Conjectures from _Colin Barker_, Aug 25 2018: (Start)
%F A224001 G.f.: x*(27 - 32*x - 56*x^2 + 164*x^3 - 159*x^4 + 85*x^5 - 32*x^6 + 9*x^7 - x^8) / (1 - x)^7.
%F A224001 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>9.
%F A224001 (End)
%e A224001 Some solutions for n=3:
%e A224001 ..1..2..2....0..1..2....0..1..1....1..2..2....0..0..0....0..0..2....2..2..2
%e A224001 ..0..1..2....1..2..2....0..1..2....1..1..2....0..1..2....0..0..0....2..2..2
%e A224001 ..1..1..1....2..2..2....0..1..1....1..1..1....0..1..1....0..1..2....1..2..2
%Y A224001 Cf. A223999.
%K A224001 nonn
%O A224001 1,1
%A A224001 _R. H. Hardin_, Mar 30 2013