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A224354 Number of 3 X n 0..2 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

%I A224354 #7 Aug 29 2018 15:24:39
%S A224354 27,216,788,2321,5840,13052,26610,50423,90012,152912,249120,391589,
%T A224354 596768,885188,1282094,1818123,2530028,3461448,4663724,6196761,
%U A224354 8129936,10543052,13527338,17186495,21637788,27013184,33460536,41144813,50249376
%N A224354 Number of 3 X n 0..2 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.
%C A224354 Row 3 of A224353.
%H A224354 R. H. Hardin, <a href="/A224354/b224354.txt">Table of n, a(n) for n = 1..210</a>
%F A224354 Empirical: a(n) = (23/360)*n^6 + (19/40)*n^5 + (235/72)*n^4 + (61/8)*n^3 + (1921/180)*n^2 + (189/10)*n + 3 for n>1.
%F A224354 Conjectures from _Colin Barker_, Aug 29 2018: (Start)
%F A224354 G.f.: x*(27 + 27*x - 157*x^2 + 396*x^3 - 474*x^4 + 326*x^5 - 116*x^6 + 17*x^7) / (1 - x)^7.
%F A224354 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>8.
%F A224354 (End)
%e A224354 Some solutions for n=3:
%e A224354 ..0..0..1....1..1..2....2..2..2....0..2..2....0..1..1....1..1..1....0..1..2
%e A224354 ..1..1..2....1..1..2....2..2..2....1..1..1....1..1..2....1..1..2....1..1..1
%e A224354 ..1..2..2....0..1..1....1..1..2....1..1..1....0..0..0....0..2..2....1..1..2
%Y A224354 Cf. A224353.
%K A224354 nonn
%O A224354 1,1
%A A224354 _R. H. Hardin_, Apr 04 2013