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 A229439 Number of n X 2 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing. 1

%I

%S 4,7,13,25,47,84,142,228,350,517,739,1027,1393,1850,2412,3094,3912,

%T 4883,6025,7357,8899,10672,12698,15000,17602,20529,23807,27463,31525,

%U 36022,40984,46442,52428,58975,66117,73889,82327,91468,101350,112012,123494

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

%H R. H. Hardin, <a href="/A229439/b229439.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/24)*n^4 + (1/12)*n^3 - (1/24)*n^2 + (23/12)*n + 2.

%F Conjectures from _Colin Barker_, Sep 16 2018: (Start)

%F G.f.: x*(4 - 13*x + 18*x^2 - 10*x^3 + 2*x^4) / (1 - x)^5.

%F 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 (End)

%e Some solutions for n=4:

%e ..0..2....0..2....0..2....1..1....0..2....0..2....0..2....0..0....0..2....0..2

%e ..0..2....0..2....1..0....1..1....1..0....0..2....0..2....1..1....1..0....0..2

%e ..0..2....0..2....2..1....1..1....1..0....1..0....1..0....2..2....2..1....1..0

%e ..0..2....1..0....2..1....1..1....1..1....1..1....1..0....2..2....2..2....2..1

%Y Column 2 of A229445.

%K nonn

%O 1,1

%A _R. H. Hardin_, Sep 23 2013

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Last modified March 25 07:48 EDT 2023. Contains 361511 sequences. (Running on oeis4.)