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A229422 Number of n X 2 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, rows lexicographically nondecreasing, and columns lexicographically nonincreasing.

%I A229422 #8 Sep 15 2018 08:45:07
%S A229422 5,12,27,55,102,175,282,432,635,902,1245,1677,2212,2865,3652,4590,
%T A229422 5697,6992,8495,10227,12210,14467,17022,19900,23127,26730,30737,35177,
%U A229422 40080,45477,51400,57882,64957,72660,81027,90095,99902,110487,121890,134152
%N A229422 Number of n X 2 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, rows lexicographically nondecreasing, and columns lexicographically nonincreasing.
%H A229422 R. H. Hardin, <a href="/A229422/b229422.txt">Table of n, a(n) for n = 1..210</a>
%F A229422 Empirical: a(n) = (1/24)*n^4 + (5/12)*n^3 + (11/24)*n^2 + (25/12)*n + 2.
%F A229422 Conjectures from _Colin Barker_, Sep 15 2018: (Start)
%F A229422 G.f.: x*(5 - 13*x + 17*x^2 - 10*x^3 + 2*x^4) / (1 - x)^5.
%F A229422 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
%F A229422 (End)
%e A229422 Some solutions for n=4:
%e A229422 ..0..0....0..0....1..0....0..0....1..1....1..0....0..0....0..0....2..2....0..0
%e A229422 ..0..0....1..0....1..0....0..0....2..1....2..1....0..0....1..1....2..2....1..1
%e A229422 ..1..1....1..1....1..1....0..0....2..1....2..1....1..0....1..1....2..2....2..2
%e A229422 ..2..2....2..1....2..1....1..1....2..2....2..1....1..0....2..1....2..2....2..2
%Y A229422 Column 2 of A229428.
%K A229422 nonn
%O A229422 1,1
%A A229422 _R. H. Hardin_, Sep 22 2013