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A264570 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.

%I A264570 #8 Jan 08 2019 19:00:20
%S A264570 1,2,4,8,24,64,160,384,960,2432,6144,15360,38400,96256,241664,606208,
%T A264570 1519616,3809280,9551872,23953408,60063744,150601728,377618432,
%U A264570 946864128,2374238208,5953290240,14927527936,37429968896,93853843456,235334008832
%N A264570 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.
%H A264570 R. H. Hardin, <a href="/A264570/b264570.txt">Table of n, a(n) for n = 1..210</a>
%F A264570 Empirical: a(n) = 2*a(n-1) + 8*a(n-4).
%F A264570 Empirical g.f.: x / (1 - 2*x - 8*x^4). - _Colin Barker_, Jan 08 2019
%e A264570 Some solutions for n=4:
%e A264570 ..1..2..6..7..8....1..2..3..4..8....1..2..3..7..8....1..5..6..7..8
%e A264570 ..0.10.11..3..4....0.10.11.12.13....0.10.11.12..4....0.10..2..3..4
%e A264570 ..5.12.13.14..9....5..6..7.14..9....5..6.13.14..9...11.12.13.14..9
%Y A264570 Row 2 of A264569.
%K A264570 nonn
%O A264570 1,2
%A A264570 _R. H. Hardin_, Nov 17 2015