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A263812 Number of (n+1) X (2+1) arrays of permutations of 0..n*3+2 with each element having index change (+-,+-) 0,0 0,1 0,2 or 1,0.

%I A263812 #10 Jan 03 2019 05:41:07
%S A263812 82,948,11305,134028,1590733,18875976,223995034,2658056430,
%T A263812 31542099589,374297467464,4441638405853,52707146757882,
%U A263812 625454634139210,7422020035297392,88074143832191077,1045140645645600804
%N A263812 Number of (n+1) X (2+1) arrays of permutations of 0..n*3+2 with each element having index change (+-,+-) 0,0 0,1 0,2 or 1,0.
%H A263812 R. H. Hardin, <a href="/A263812/b263812.txt">Table of n, a(n) for n = 1..210</a>
%F A263812 Empirical: a(n) = 10*a(n-1) + 23*a(n-2) - 10*a(n-3) -a(n-4).
%F A263812 Empirical g.f.: x*(82 + 128*x - 61*x^2 - 6*x^3) / (1 - 10*x - 23*x^2 + 10*x^3 + x^4). - _Colin Barker_, Jan 03 2019
%e A263812 Some solutions for n=4:
%e A263812 ..2..0..1....2..0..1....0..2..1....2..1..0....1..0..2....0..4..1....2..0..1
%e A263812 ..3..5..4....6..3..4....3..7..5....5..3..8....5..7..4....3..5..2....3..5..4
%e A263812 ..7..6.11....7..8..5....8..4..6....9..4..7....3..8..6....7..8.11....9..6..8
%e A263812 .10.13..8...10.11..9...12..9.14....6.11.10...12.13.14....6..9.10...10..7.11
%e A263812 ..9.12.14...12.13.14...13.10.11...13.12.14....9.10.11...12.14.13...14.13.12
%Y A263812 Column 2 of A263816.
%K A263812 nonn
%O A263812 1,1
%A A263812 _R. H. Hardin_, Oct 27 2015