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A224355 Number of 4 X n 0..2 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.

%I A224355 #7 Aug 29 2018 16:58:19
%S A224355 81,1296,5880,19608,57387,151010,363392,810436,1693423,3344982,
%T A224355 6292120,11340202,19682181,33037788,53827802,85388930,132235237,
%U A224355 200372476,297672078,434311972,623291815,881030622,1228055196,1689788168
%N A224355 Number of 4 X n 0..2 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.
%C A224355 Row 4 of A224353.
%H A224355 R. H. Hardin, <a href="/A224355/b224355.txt">Table of n, a(n) for n = 1..210</a>
%F A224355 Empirical: a(n) = (41/4032)*n^8 + (9/112)*n^7 + (239/288)*n^6 + (109/24)*n^5 + (12079/576)*n^4 + (39/16)*n^3 + (310151/1008)*n^2 - (21299/84)*n + 142 for n>3.
%F A224355 Conjectures from _Colin Barker_, Aug 29 2018: (Start)
%F A224355 G.f.: x*(81 + 567*x - 2868*x^2 + 6540*x^3 - 6063*x^4 - 415*x^5 + 7550*x^6 - 8564*x^7 + 4918*x^8 - 1584*x^9 + 262*x^10 - 14*x^11) / (1 - x)^9.
%F A224355 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>12.
%F A224355 (End)
%e A224355 Some solutions for n=3:
%e A224355 ..2..2..2....0..1..2....0..0..0....0..2..2....0..2..2....0..1..1....1..2..2
%e A224355 ..1..1..2....0..2..2....0..0..0....1..1..1....0..1..1....1..2..2....1..1..1
%e A224355 ..1..1..1....0..0..1....0..0..2....0..1..2....0..1..1....1..1..2....0..1..2
%e A224355 ..0..1..1....0..1..2....0..0..0....0..1..2....0..0..1....0..1..2....0..0..0
%Y A224355 Cf. A224353.
%K A224355 nonn
%O A224355 1,1
%A A224355 _R. H. Hardin_, Apr 04 2013