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A264514 Number of (2n) X (2+1) arrays of permutations of 0..n*6-1 with each element having directed index change -1,0 0,2 -1,-2 or 1,0.

%I A264514 #8 Jan 08 2019 08:23:13
%S A264514 1,3,12,46,177,684,2640,10180,39249,151326,583444,2249491,8673001,
%T A264514 33439105,128925825,497078745,1916507251,7389171396,28489249854,
%U A264514 109841457681,423498192724,1632814449360,6295382298780,24272101648369
%N A264514 Number of (2n) X (2+1) arrays of permutations of 0..n*6-1 with each element having directed index change -1,0 0,2 -1,-2 or 1,0.
%H A264514 R. H. Hardin, <a href="/A264514/b264514.txt">Table of n, a(n) for n = 1..105</a>
%F A264514 Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 13*a(n-3) - 11*a(n-4) + 6*a(n-5) - a(n-6).
%F A264514 Empirical g.f.: x*(1 - 3*x + 5*x^2 - 6*x^3 + 5*x^4 - x^5) / (1 - 6*x + 11*x^2 - 13*x^3 + 11*x^4 - 6*x^5 + x^6). - _Colin Barker_, Jan 08 2019
%e A264514 Some solutions for n=3:
%e A264514 ..5..4..0....3..4..0....3..4..5....3..4..0....5..4..0....3..4..5....3..4..0
%e A264514 ..8..1..2....8..1..2....0..1..2....6..1..2....8..1..2....0..1..2....8..1..2
%e A264514 ..3.10..6...11.10..5....9.10.11....9.10..5....3.10.11....9.10..6....9.10..5
%e A264514 .14..7..9....6..7.14....6..7..8...14..7..8....6..7.14...14..7..8....6..7.14
%e A264514 .17.16.11....9.16.17...15.16.17...17.16.11....9.16.17...17.16.11...17.16.11
%e A264514 .12.13.15...12.13.15...12.13.14...12.13.15...12.13.15...12.13.15...12.13.15
%Y A264514 Column 2 of A264520 (nonzero terms only).
%K A264514 nonn
%O A264514 1,2
%A A264514 _R. H. Hardin_, Nov 16 2015