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A264380 Number of (2+1) X (n+1) arrays of permutations of 0..n*3+2 with each element having directed index change 2,-2 -1,0 -1,2 1,0 or 0,-1.

%I A264380 #8 Jan 07 2019 19:15:22
%S A264380 0,1,6,9,61,121,544,1357,5100,14340,49324,147230,485141,1491460,
%T A264380 4812843,15012153,47950974,150636184,478755674,1509249756,4785018013,
%U A264380 15110309428,47849311565,151226992088,478604645313,1513243349293,4787751445331
%N A264380 Number of (2+1) X (n+1) arrays of permutations of 0..n*3+2 with each element having directed index change 2,-2 -1,0 -1,2 1,0 or 0,-1.
%H A264380 R. H. Hardin, <a href="/A264380/b264380.txt">Table of n, a(n) for n = 1..210</a>
%F A264380 Empirical: a(n) = 2*a(n-1) + 5*a(n-2) - 6*a(n-3) + 7*a(n-4) - 4*a(n-5) - a(n-6) + 5*a(n-7) - 4*a(n-8) + 2*a(n-9) - a(n-10).
%F A264380 Empirical g.f.: x^2*(1 + 4*x - 8*x^2 + 19*x^3 - 17*x^4 + 13*x^5 - 8*x^6 + 2*x^7 - x^8) / (1 - 2*x - 5*x^2 + 6*x^3 - 7*x^4 + 4*x^5 + x^6 - 5*x^7 + 4*x^8 - 2*x^9 + x^10). - _Colin Barker_, Jan 07 2019
%e A264380 Some solutions for n=4:
%e A264380 ..1..6..5..4..7....1..2..3..8..7....5..6..3..8..7....5..2..3..8..7
%e A264380 ..0.11.10..3.14....0.11.10.13.12....0..1.10.11..4....0..1.10.13.12
%e A264380 ..2.12.13..8..9....5..6..4.14..9....2.12.13.14..9...11..6..4.14..9
%Y A264380 Row 2 of A264379.
%K A264380 nonn
%O A264380 1,3
%A A264380 _R. H. Hardin_, Nov 12 2015