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A264366 Number of (2+1) X (n+1) arrays of permutations of 0..n*3+2 with each element having directed index change 0,0 0,2 1,0 or -1,-2.

%I A264366 #8 Jan 07 2019 12:39:56
%S A264366 1,6,36,120,400,1440,5184,18432,65536,233472,831744,2962176,10549504,
%T A264366 37572864,133818624,476601600,1697440000,6045523200,21531453696,
%U A264366 76685407488,273119121664,972728179968,3464422799616,12338724758784
%N A264366 Number of (2+1) X (n+1) arrays of permutations of 0..n*3+2 with each element having directed index change 0,0 0,2 1,0 or -1,-2.
%H A264366 R. H. Hardin, <a href="/A264366/b264366.txt">Table of n, a(n) for n = 1..210</a>
%F A264366 Empirical: a(n) = 3*a(n-1) + 6*a(n-3) + 4*a(n-4).
%F A264366 Empirical g.f.: x*(1 + 3*x + 18*x^2 + 6*x^3) / ((1 + 2*x^2)*(1 - 3*x - 2*x^2)). -  _Colin Barker_, Jan 07 2019
%e A264366 Some solutions for n=4:
%e A264366 ..0..8..2..1..4....0..8..9..3..4....0..8..2..3..4....7..1..0..3..2
%e A264366 ..5..6.14..3..7...12..1..2..6..7....5..1..7..6..9....5..6.14..8..4
%e A264366 .10.11.12.13..9....5.11.10.13.14...10.11.12.13.14...10.11.12.13..9
%Y A264366 Row 2 of A264364.
%K A264366 nonn
%O A264366 1,2
%A A264366 _R. H. Hardin_, Nov 12 2015