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A264677 Number of (2+1) X (n+1) arrays of permutations of 0..n*3+2 with each element having directed index change -1,-1 1,0 -1,-2 -2,-2 or 0,1.

%I A264677 #7 Jan 08 2019 15:19:14
%S A264677 1,2,10,29,75,201,588,1700,4785,13401,37905,107598,304638,860789,
%T A264677 2433555,6885713,19483112,55110392,155875521,440924465,1247301569,
%U A264677 3528321578,9980556450,28232081677,79861067099,225905953689,639026458132
%N A264677 Number of (2+1) X (n+1) arrays of permutations of 0..n*3+2 with each element having directed index change -1,-1 1,0 -1,-2 -2,-2 or 0,1.
%H A264677 R. H. Hardin, <a href="/A264677/b264677.txt">Table of n, a(n) for n = 1..210</a>
%F A264677 Empirical: a(n) = 3*a(n-1) - 3*a(n-2) + 5*a(n-3) + 7*a(n-4) - 5*a(n-5) + 7*a(n-6) - 3*a(n-7) + a(n-8) - a(n-9).
%F A264677 Empirical g.f.: x*(1 - x + 7*x^2 + x^4 + 4*x^5 - 2*x^6 - x^8) / (1 - 3*x + 3*x^2 - 5*x^3 - 7*x^4 + 5*x^5 - 7*x^6 + 3*x^7 - x^8 + x^9). - _Colin Barker_, Jan 08 2019
%e A264677 Some solutions for n=4:
%e A264677 .12..7..9..2..3....6..7..1..2..3....6.13..8..2..3...12..0..1..2..3
%e A264677 ..0..1..6.14..4....0.12.13.14..4....0..1.14..7..4...11.13..6.14..4
%e A264677 ..5.10.11..8.13....5.10.11..8..9....5.10.11.12..9....5.10..7..8..9
%Y A264677 Row 2 of A264676.
%K A264677 nonn
%O A264677 1,2
%A A264677 _R. H. Hardin_, Nov 20 2015