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A264054 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,-2.

%I A264054 #10 Mar 20 2018 20:37:42
%S A264054 2,8,18,45,125,320,832,2197,5733,14994,39304,102850,269225,704969,
%T A264054 1845504,4831488,12649337,33116057,86698690,226981000,594243090,
%U A264054 1555747893,4073003173,10663258432,27916771136,73087061741,191344405725
%N A264054 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,-2.
%C A264054 Column 2 of A264059.
%H A264054 R. H. Hardin, <a href="/A264054/b264054.txt">Table of n, a(n) for n = 1..210</a>
%F A264054 Empirical: a(n) = 3*a(n-1) - a(n-2) + 3*a(n-3) - 9*a(n-4) + 3*a(n-5) - a(n-6) + 3*a(n-7) - a(n-8).
%F A264054 Empirical g.f.: x*(2 + 2*x - 4*x^2 - 7*x^3 + 2*x^4 + 2*x^5 + 2*x^6 - x^7) / ((1 - 3*x + x^2)*(1 - 3*x^3 + x^6)). - _Colin Barker_, Mar 20 2018
%e A264054 Some solutions for n=4:
%e A264054 ..5..1..6....5..1..6....0..1..6....0..1..6....5..1..2....0..1..2....5..1..6
%e A264054 ..3..4..0....3..4..0....8..4..5....3..4..5....8..4..0....8..4..9....3..4..0
%e A264054 ..2..7..8....2..7.12....2..7..3....2..7.12...11..7..3...11..7..3....2..7.12
%e A264054 .14.10.11...14.10.11....9.10.11....9.10.11....9.10..6....5.10..6....9.10.11
%e A264054 .12.13..9....8.13..9...12.13.14....8.13.14...12.13.14...12.13.14....8.13.14
%Y A264054 Cf. A264059.
%K A264054 nonn
%O A264054 1,1
%A A264054 _R. H. Hardin_, Nov 02 2015