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A264629 Number of (2+1) X (n+1) arrays of permutations of 0..n*3+2 with each element having directed index change -2,0 -1,0 0,-1 or 1,1.

%I A264629 #7 Jan 08 2019 15:11:19
%S A264629 1,2,4,9,16,37,76,160,337,704,1485,3110,6532,13713,28784,60441,126872,
%T A264629 266368,559201,1173968,2464617,5174122,10862468,22804377,47874976,
%U A264629 100507613,211003236,442975264,929971633,1952360368,4098738901
%N A264629 Number of (2+1) X (n+1) arrays of permutations of 0..n*3+2 with each element having directed index change -2,0 -1,0 0,-1 or 1,1.
%H A264629 R. H. Hardin, <a href="/A264629/b264629.txt">Table of n, a(n) for n = 1..210</a>
%F A264629 Empirical: a(n) = 2*a(n-1) + 2*a(n-5) - 2*a(n-6) + 4*a(n-7) - a(n-10).
%F A264629 Empirical g.f.: x*(1 + x^3 - 2*x^4 + 3*x^5 - x^8) / (1 - 2*x - 2*x^5 + 2*x^6 - 4*x^7 + x^10). - _Colin Barker_, Jan 08 2019
%e A264629 Some solutions for n=4:
%e A264629 ..1..6..3..4..9....1..6..7..4..9...10..2.12..4.14....5..2..7..4..9
%e A264629 .10..0.12..2.14...10..0.12..2..3....6..0..1..9..3...10..0..1.13..3
%e A264629 .11..5.13..7..8...11..5.13.14..8...11..5.13..7..8...11.12..6.14..8
%Y A264629 Row 2 of A264628.
%K A264629 nonn
%O A264629 1,2
%A A264629 _R. H. Hardin_, Nov 19 2015