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%I #10 Jan 04 2019 17:38:06
%S 2,9,45,200,845,3549,14994,63525,269225,1140624,4831721,20466953,
%T 86698690,367261713,1555747893,6590256856,27916775317,118257348165,
%U 500946152850,2122041959565,8989114033297,38078498156832,161303106660625
%N Number of (n+1) X (2+1) arrays of permutations of 0..n*3+2 with each element having index change +-(.,.) 0,0 1,-2 or 2,-1.
%H R. H. Hardin, <a href="/A264122/b264122.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 4*a(n-1) + a(n-2) - 4*a(n-3) + 16*a(n-4) + 4*a(n-5) + a(n-6) - 4*a(n-7) - a(n-8).
%F Empirical g.f.: x*(2 + x + 7*x^2 + 19*x^3 + 4*x^4 - 3*x^5 - 5*x^6 - x^7) / ((1 + x - x^2)*(1 - 4*x - x^2)*(1 - x + 2*x^2 + x^3 + x^4)). - _Colin Barker_, Jan 04 2019
%e Some solutions for n=4:
%e ..0..6..3....0..6..7....0..1..2....0..6..2....0..1..2....0..6..2....0..6..3
%e ..2..9..5....3..9..5....3..4..6....3..9.10....3..4..6....3..4..5....2..9.10
%e ..1..7..8....1..2..8....5..7.13....1..7..8....5.12.13....1.12.13....1..7..8
%e ..4.10.12....4.10.12....9.10.12....4..5.12....9.10.11....9.10.11....4..5.11
%e .11.13.14...11.13.14...11..8.14...11.13.14....7..8.14....7..8.14...12.13.14
%Y Column 2 of A264128.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 03 2015
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