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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 0,0 1,1 0,-1 -1,1 or 0,-2.
1

%I #11 Jan 06 2019 07:56:45

%S 8,21,89,296,1105,3897,14128,50533,181937,652944,2346977,8429681,

%T 30288280,108807669,390915337,1404388408,5045461169,18126337449,

%U 65121053504,233954670533,840509324641,3019625618976,10848352515265

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

%H R. H. Hardin, <a href="/A264238/b264238.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) + 6*a(n-2) - a(n-3).

%F Empirical g.f.: x*(8 + 5*x - x^2) / (1 - 2*x - 6*x^2 + x^3). - _Colin Barker_, Jan 06 2019

%e Some solutions for n=4:

%e ..2..3..4....0..1..2....0..1..2....1..2..4....2..3..4....1..3..2....2..1..4

%e ..5..0..1....3..4..5....3..6..5....5..0..7....5..0..1....4..0..5....5..0..7

%e ..6..7..8....6..8.10....8..9..4....6..3..8....6..8.10....8..9.10....6..3..8

%e .10.12.11...11.12..7...11.10..7...10.11.13...11.12..7...11..6..7....9.10.11

%e .13..9.14...13..9.14...12.13.14...12..9.14...13..9.14...12.13.14...12.13.14

%Y Column 2 of A264244.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 09 2015