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Number of (n+1) X (2+1) arrays of permutations of 0..n*3+2 with each element having directed index change -1,1 -1,2 1,0 or 0,-1.
1

%I #8 Jan 08 2019 19:00:32

%S 1,2,5,10,21,44,93,196,413,870,1833,3862,8137,17144,36121,76104,

%T 160345,337834,711789,1499682,3159709,6657252,14026293,29552268,

%U 62264245,131185742,276397777,582347822,1226959889,2585105520,5446608817

%N Number of (n+1) X (2+1) arrays of permutations of 0..n*3+2 with each element having directed index change -1,1 -1,2 1,0 or 0,-1.

%H R. H. Hardin, <a href="/A264544/b264544.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) + a(n-4).

%F Empirical g.f.: x*(1 + x^2) / (1 - 2*x - x^4). - _Colin Barker_, Jan 08 2019

%e Some solutions for n=4:

%e ..1..2..4....1..2..3....1..2..4....1..2..4....1..3..4....1..2..4....1..3..4

%e ..0..6..7....0..5..6....0..5..7....0..6..7....0..5..2....0..5..7....0..6..2

%e ..3..8..5....7..4..9....3..9.10....3..9..5....7..8.10....3..8.10....7..8..5

%e .10.12.13...10.12..8....6.12..8...10.12..8....6.12.13....6.12.13...10.12.13

%e ..9.14.11...13.14.11...13.14.11...13.14.11....9.14.11....9.14.11....9.14.11

%Y Column 2 of A264550.

%K nonn

%O 1,2

%A _R. H. Hardin_, Nov 17 2015