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

%I #8 Jan 08 2019 19:00:51

%S 1,2,4,10,16,56,128,320,784,1792,4480,10496,25600,62080,149504,363520,

%T 872448,2109440,5088256,12279808,29683712,71622656,173031424,

%U 417669120,1008336896,2434695168,5877530624,14192476160,34265432064,82732646400

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

%H R. H. Hardin, <a href="/A264585/b264585.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) + 16*a(n-5) - 16*a(n-6) + 32*a(n-7) - 64*a(n-10).

%F Empirical g.f.: x*(1 + 2*x^3 - 4*x^4 + 8*x^5 - 16*x^8) / (1 - 2*x - 16*x^5 + 16*x^6 - 32*x^7 + 64*x^10). - _Colin Barker_, Jan 08 2019

%e Some solutions for n=4:

%e ..1..2..3..7..8....1..5..3..4..8....1..5..3..7..8....1..5..6..4..8

%e ..0.10.11.12..4....6.10..0..9..2....0.10..2.12..4....0.10..2..3.13

%e ..5..6.13.14..9...11.12.13.14..7...11..6.13.14..9...11.12..7.14..9

%Y Row 2 of A264583.

%K nonn

%O 1,2

%A _R. H. Hardin_, Nov 18 2015