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A264266 Number of (n+1) X (2+1) arrays of permutations of 0..n*3+2 with each element having index change +-(.,.) 0,0 1,0 or 1,2.

%I A264266 #9 Jan 07 2019 05:57:30
%S A264266 10,48,305,1800,10933,65856,397970,2402455,14508869,87609600,
%T A264266 529045373,3194668217,19291314050,116492151552,703447966957,
%U A264266 4247829912600,25650883291001,154895038005840,935346867163930,5648171599648271
%N A264266 Number of (n+1) X (2+1) arrays of permutations of 0..n*3+2 with each element having index change +-(.,.) 0,0 1,0 or 1,2.
%H A264266 R. H. Hardin, <a href="/A264266/b264266.txt">Table of n, a(n) for n = 1..210</a>
%F A264266 Empirical: a(n) = 4*a(n-1) + 16*a(n-2) - 16*a(n-3) - 41*a(n-4) + 16*a(n-5) + 16*a(n-6) - 4*a(n-7) - a(n-8).
%F A264266 Empirical g.f.: x*(10 + 8*x - 47*x^2 - 28*x^3 + 31*x^4 + 12*x^5 - 5*x^6 - x^7) / ((1 + x - x^2)*(1 - x - x^2)*(1 - 4*x - 13*x^2 + 4*x^3 + x^4)). - _Colin Barker_, Jan 07 2019
%e A264266 Some solutions for n=4:
%e A264266 ..3..4..2....5..1..2....0..4..5....3..1..2....0..1..2....3..4..5....3..1..2
%e A264266 ..0..1..5....0..7..8....3..1..2....0..4..5....3..7..8....0..1..2....8..7..0
%e A264266 ..9..7..8....6..4..3....9..7.11....6..7.11....6..4..5....6.10..8...11..4..5
%e A264266 .14.13..6...14.13.11....6.13..8...12.13..8....9.10.14...12..7.11...12.10..6
%e A264266 .12.10.11...12.10..9...12.10.14....9.10.14...12.13.11....9.13.14....9.13.14
%Y A264266 Column 2 of A264272.
%K A264266 nonn
%O A264266 1,1
%A A264266 _R. H. Hardin_, Nov 10 2015