A264332 - OEIS

%I #8 Jan 07 2019 11:17:15

%S 1,8,40,240,1528,8976,51904,302328,1757848,10199400,59182576,

%T 343432200,1992680992,11561675184,67081902808,389213984040,

%U 2258240299432,13102425739632,76020937882840,441077255457840,2559151966018144

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

%H R. H. Hardin, <a href="/A264332/b264332.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-1) - 5*a(n-2) + 36*a(n-3) - 72*a(n-4) - 243*a(n-6) for n>7.

%F Empirical g.f.: x*(1 + 2*x - 3*x^2 + 4*x^3 + 72*x^4 + 144*x^5 + 171*x^6) / ((1 - x - 9*x^3)*(1 - 5*x - 27*x^3)). - _Colin Barker_, Jan 07 2019

%e Some solutions for n=4:

%e ..1..5..6..7..8....1..2..6..7..8....1..5..6..7..8....1..5..3..7..8

%e ..0..2..3.12..4....0.10..3..4.13....0..2..3.12..4....0.10..2..4.13

%e .11.15.16.14..9....5.15.16.14..9...11.15.16.14..9....6.12.16..9.18

%e .10.20.13.22.23...11.20.12.22.23...10.20.18.13.23...11.20.21.22.14

%e .21.17.18.24.19...21.17.18.24.19...21.22.17.24.19...15.17.23.24.19

%Y Column 4 of A264336.

%K nonn

%O 1,2

%A _R. H. Hardin_, Nov 11 2015