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A264565 Number of (n+1) X (4+1) arrays of permutations of 0..n*5+4 with each element having directed index change 1,0 1,1 0,-1 or -1,1.

%I A264565 #8 Jan 08 2019 12:30:01
%S A264565 2,8,44,192,888,4104,18540,85752,389340,1787832,8158644,37336464,
%T A264565 170669592,780379920,3568245048,16314092712,74594729628,341056001520,
%U A264565 1559406670200,7129910871000,32599645712604,149052729608136
%N A264565 Number of (n+1) X (4+1) arrays of permutations of 0..n*5+4 with each element having directed index change 1,0 1,1 0,-1 or -1,1.
%H A264565 R. H. Hardin, <a href="/A264565/b264565.txt">Table of n, a(n) for n = 1..210</a>
%F A264565 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 A264565 Empirical g.f.: 2*x*(1 + 4*x + 4*x^2 - 12*x^3 - 51*x^4 - 72*x^5 - 81*x^6) / ((1 - 3*x^2 - 9*x^3)*(1 - 15*x^2 - 27*x^3)). - _Colin Barker_, Jan 08 2019
%e A264565 Some solutions for n=4:
%e A264565 ..1..2..3..7..8....1..5..6..7..8....1..5..6..7..8....1..5..3..7..8
%e A264565 ..0.10.11..9..4....0.10..2..3..4....0.10..2..3..4....6..0..2.12..4
%e A264565 ..5..6.13.14.18...11.15.13.17..9...11.12.13.17..9...11.15.16.14..9
%e A264565 .16.20.12.22.23...16.20.12.19.14...16.20.18.22.14...10.20.18.13.23
%e A264565 .21.15.17.24.19...21.22.23.24.18...21.15.23.24.19...21.22.17.24.19
%Y A264565 Column 4 of A264569.
%K A264565 nonn
%O A264565 1,1
%A A264565 _R. H. Hardin_, Nov 17 2015