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A264472 Number of (n+1) X (4+1) arrays of permutations of 0..n*5+4 with each element having directed index change 0,1 1,0 2,1 or -1,-1.

%I A264472 #9 Jan 08 2019 06:45:36
%S A264472 0,8,16,120,456,2232,10116,45792,212112,960336,4418388,20134008,
%T A264472 92208780,421315344,1926779076,8809428456,40277366640,184164908040,
%U A264472 842016117672,3849965354232,17602701446772,80483933441520,367989633268848
%N A264472 Number of (n+1) X (4+1) arrays of permutations of 0..n*5+4 with each element having directed index change 0,1 1,0 2,1 or -1,-1.
%H A264472 R. H. Hardin, <a href="/A264472/b264472.txt">Table of n, a(n) for n = 1..210</a>
%F A264472 Empirical: a(n) = 18*a(n-2) + 36*a(n-3) - 45*a(n-4) - 216*a(n-5) - 243*a(n-6) for n>7.
%F A264472 Empirical g.f.: 4*x^2*(2 + 4*x - 6*x^2 - 30*x^3 - 36*x^4 + 9*x^5) / ((1 - 3*x^2 - 9*x^3)*(1 - 15*x^2 - 27*x^3)). - _Colin Barker_, Jan 08 2019
%e A264472 Some solutions for n=4:
%e A264472 ..6..0..8..9..3....6..7..1..2..3....6..7..8..2..3....6..7..1..2..3
%e A264472 .11..5..2..7..4....0..5.13.14..4....0..1.13.14..4....0..5.13.14..4
%e A264472 .16.10..1.12.13...16.10.11.12..9...16.17.11.19..9...16.10.11.19..9
%e A264472 .21.22.23.24.14...21.22.23.24..8...10..5.12.24.18...21.22.12.24..8
%e A264472 .15.20.17.18.19...15.20.17.18.19...15.20.21.22.23...15.20.17.18.23
%Y A264472 Column 4 of A264476.
%K A264472 nonn
%O A264472 1,2
%A A264472 _R. H. Hardin_, Nov 14 2015