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A229442 Number of n X 5 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing.

%I A229442 #8 Sep 17 2018 08:31:42
%S A229442 7,19,60,212,753,2546,8024,23428,63430,159945,377840,841419,1777036,
%T A229442 3578998,6908102,12834739,23041529,40103959,67871516,111976374,
%U A229442 180501843,284848554,440842772,670138334,1001971536,1475336877,2141660944
%N A229442 Number of n X 5 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing.
%H A229442 R. H. Hardin, <a href="/A229442/b229442.txt">Table of n, a(n) for n = 1..210</a>
%F A229442 Empirical: a(n) = (1/103680)*n^10 + (1/80640)*n^9 + (1/12096)*n^8 + (47/13440)*n^7 + (11/6912)*n^6 + (173/3840)*n^5 + (1187/10368)*n^4 + (12437/20160)*n^3 - (6211/10080)*n^2 + (4901/840)*n + 1.
%F A229442 Conjectures from _Colin Barker_, Sep 17 2018: (Start)
%F A229442 G.f.: x*(7 - 58*x + 236*x^2 - 558*x^3 + 896*x^4 - 941*x^5 + 709*x^6 - 343*x^7 + 103*x^8 - 17*x^9 + x^10) / (1 - x)^11.
%F A229442 a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11) for n>11.
%F A229442 (End)
%e A229442 Some solutions for n=4:
%e A229442 ..0..0..0..0..2....0..2..2..2..2....0..0..2..2..2....0..2..2..2..2
%e A229442 ..0..0..0..0..2....1..0..2..2..2....1..1..0..2..2....1..0..2..2..2
%e A229442 ..1..1..1..1..0....1..1..0..2..2....1..1..1..0..0....1..1..0..0..0
%e A229442 ..1..1..1..1..1....1..1..0..2..2....1..1..1..1..1....1..1..1..1..1
%Y A229442 Column 5 of A229445.
%K A229442 nonn
%O A229442 1,1
%A A229442 _R. H. Hardin_, Sep 23 2013