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

Row 2 of A264569.

Empirical: a(n) = 2*a(n-1) +) + 8*a(n-4)).

Empirical g.f.: x / (1 - 2*x - 8*x^4). - Colin Barker, Jan 08 2019

Some solutions for n=4:

Cf. Row 2 of A264569.

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R. H. Hardin, <a href="/A264570/b264570.txt">Table of n, a(n) for n = 1..210</a>

allocated for R. H. Hardin

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

1, 2, 4, 8, 24, 64, 160, 384, 960, 2432, 6144, 15360, 38400, 96256, 241664, 606208, 1519616, 3809280, 9551872, 23953408, 60063744, 150601728, 377618432, 946864128, 2374238208, 5953290240, 14927527936, 37429968896, 93853843456, 235334008832

1,2

Row 2 of A264569.

Empirical: a(n) = 2*a(n-1) +8*a(n-4)

Some solutions for n=4

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

..0.10.11..3..4....0.10.11.12.13....0.10.11.12..4....0.10..2..3..4

..5.12.13.14..9....5..6..7.14..9....5..6.13.14..9...11.12.13.14..9

Cf. A264569.

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nonn

R. H. Hardin, Nov 17 2015

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