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A264423 Number of (2+1) X (n+1) arrays of permutations of 0..n*3+2 with each element having directed index change 0,1 2,2 1,0 -1,2 -2,-1 or -1,-1.

%I A264423 #13 Feb 18 2021 17:50:35
%S A264423 1,3,12,37,119,385,1252,4061,13166,42687,138419,448847,1455443,
%T A264423 4719435,15303308,49622768,160907641,521761825,1691873630,5486097814,
%U A264423 17789312907,57683924784,187046863084,606521298870,1966716147754,6377306803896
%N A264423 Number of (2+1) X (n+1) arrays of permutations of 0..n*3+2 with each element having directed index change 0,1 2,2 1,0 -1,2 -2,-1 or -1,-1.
%H A264423 R. H. Hardin, <a href="/A264423/b264423.txt">Table of n, a(n) for n = 1..210</a>
%F A264423 Empirical: a(n) = 3*a(n-1) + a(n-3) + 5*a(n-4) + a(n-7).
%F A264423 Empirical g.f.: x*(1 + 3*x^2 + x^5) / ((1 + x^2 + x^3)*(1 - 3*x - x^2 + x^3 - x^4)). - _Colin Barker_, Jan 07 2019
%e A264423 Some solutions for n=4:
%e A264423 ..6..7..1..2..3....6..0..1..9..3....6.12.13.14..7...11.12.13..2..3
%e A264423 ..0.12.13.14..4...11.12..2.14..4....0..1..2..3..4....0..1..6.14..4
%e A264423 ..5.10.11..8..9....5.10..7..8.13....5.10.11..8..9....5.10..7..8..9
%Y A264423 Row 2 of A264422.
%K A264423 nonn
%O A264423 1,2
%A A264423 _R. H. Hardin_, Nov 12 2015