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A264018 Number of (2+1) X (n+1) arrays of permutations of 0..n*3+2 with each element having index change +-(.,.) 0,0 1,2 or 2,2.

%I A264018 #11 Sep 09 2020 09:10:48
%S A264018 1,5,25,105,441,1869,7921,33553,142129,602069,2550409,10803705,
%T A264018 45765225,193864605,821223649,3478759201,14736260449,62423800997,
%U A264018 264431464441,1120149658761,4745030099481,20100270056685,85146110326225
%N A264018 Number of (2+1) X (n+1) arrays of permutations of 0..n*3+2 with each element having index change +-(.,.) 0,0 1,2 or 2,2.
%H A264018 R. H. Hardin, <a href="/A264018/b264018.txt">Table of n, a(n) for n = 1..210</a>
%F A264018 Empirical: a(n) = 4*a(n-1) + 4*a(n-3) + a(n-4).
%F A264018 Empirical g.f.: x*(1 + x + 5*x^2 + x^3) / ((1 + x^2)*(1 - 4*x - x^2)). - _Colin Barker_, Jan 03 2019
%F A264018 Empirical: 5*a(n) = 2*A228826(n) + A048876(n). - _R. J. Mathar_, Sep 09 2020
%e A264018 Some solutions for n=4:
%e A264018 ..7..1..2..3..4....0.13..9..3..4....0..8..9..3..4....7..1..9..3..4
%e A264018 .12..6..0..8..9...12..6..7..8..2...12..6.14..1..2...12.13..0..8..2
%e A264018 .10.11..5.13.14...10.11..5..1.14...10.11..5.13..7...10.11..5..6.14
%Y A264018 Row 2 of A264017.
%K A264018 nonn
%O A264018 1,2
%A A264018 _R. H. Hardin_, Nov 01 2015