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

%I #8 Jan 08 2019 15:11:31

%S 1,2,4,9,18,41,84,176,369,772,1625,3406,7156,15025,31542,66225,139016,

%T 291856,612705,1286296,2700433,5669210,11901844,24986425,52455914,

%U 110124697,231193116,485361376,1018956049,2139172156,4490927145

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

%H R. H. Hardin, <a href="/A264649/b264649.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) + 2*a(n-5) - 2*a(n-6) + 4*a(n-7) - a(n-10).

%F Empirical g.f.: x*(1 + x^3 + 3*x^5 - x^8) / (1 - 2*x - 2*x^5 + 2*x^6 - 4*x^7 + x^10). - _Colin Barker_, Jan 08 2019

%e Some solutions for n=4:

%e ..1..2..5....1..2..5....3..2..5....3..2..5....3..2..5....1..2..5....1..2..5

%e ..4..7..8....4..0..8....4..0..1....6..0..1....6..0..1....6..0..8....6..0..8

%e ..9.10..0....7..3.11....9..8.11....7..8..4....9..8..4....7..3..4....9..3..4

%e .12.11..3...12..6.14...12..6..7...12.11.14...12.11..7...12.11.14...12.11..7

%e .13.14..6...13..9.10...13.14.10...13..9.10...13.14.10...13..9.10...13.14.10

%Y Column 2 of A264655.

%K nonn

%O 1,2

%A _R. H. Hardin_, Nov 20 2015