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

%I #9 Jan 04 2019 09:02:22

%S 64,1448,32761,645627,12723489,252076323,4994107561,98921264827,

%T 1959392447089,38811196731923,768763293949561,15227481732752427,

%U 301622361195255489,5974464570433893123,118340784688251794761

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

%H R. H. Hardin, <a href="/A264086/b264086.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 19*a(n-1) + 304*a(n-3) + 256*a(n-4).

%F Empirical g.f.: x*(64 + 232*x + 5249*x^2 + 3712*x^3) / ((1 + 16*x^2)*(1 - 19*x - 16*x^2)). - _Colin Barker_, Jan 04 2019

%e Some solutions for n=3:

%e ..0..1..3.11..4....0..1..2..3..4....0..1..2.11..4....1..0..2..4.12

%e ..6..5.15.16.17....5..6..8..7.17....5..6..7..9..8....6..5.15..8.17

%e ..2.10.13.12.14...11.10.12.14.13...10..3.12.14.13...10..3.11.14.13

%e ..7..8..9.19.18...16.15..9.18.19...15.17.16.18.19....7.16..9.18.19

%Y Column 4 of A264090.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 03 2015