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Number of permutations of 6 copies of 1..n introduced in order 1..n with no element equal to another within a distance of 1.
9

%I #19 Nov 10 2024 21:47:03

%S 1,0,1,8142,351574834,47940557125969,16985819072511102549,

%T 13519747358522016160671387,21671513613423101256198918372909,

%U 64311863997340571475504065539218471107,330586922756304429697714946501284146322953006

%N Number of permutations of 6 copies of 1..n introduced in order 1..n with no element equal to another within a distance of 1.

%H Seiichi Manyama, <a href="/A190835/b190835.txt">Table of n, a(n) for n = 0..100</a> (terms 1..14 from R. J. Mathar)

%F a(n) ~ sqrt(6) * 324^n * n^(5*n) / (5^n * exp(5*n + 5)). - _Vaclav Kotesovec_, Nov 24 2018

%e Some solutions for n=3

%e ..1....1....1....1....1....1....1....1....1....1....1....1....1....1....1....1

%e ..2....2....2....2....2....2....2....2....2....2....2....2....2....2....2....2

%e ..3....3....1....3....1....3....3....3....1....1....3....3....3....3....3....3

%e ..2....2....3....2....3....2....2....1....2....3....1....1....2....2....2....1

%e ..1....3....2....3....2....1....3....3....1....2....3....3....3....3....1....2

%e ..2....1....3....1....3....3....1....2....3....3....2....2....2....1....3....1

%e ..3....2....1....2....1....2....3....3....1....2....3....3....1....2....2....2

%e ..2....1....3....3....3....1....2....2....3....3....1....1....3....3....3....3

%e ..3....2....2....1....2....2....1....3....2....2....2....3....1....2....2....2

%e ..1....3....3....3....3....3....2....1....3....1....1....1....3....1....1....1

%e ..3....1....2....2....2....1....1....3....2....3....2....2....2....3....3....3

%e ..1....2....1....3....1....3....2....1....3....1....1....3....1....2....1....1

%e ..3....3....2....2....3....1....1....2....2....2....3....2....2....1....2....2

%e ..1....1....3....1....2....3....3....3....1....3....2....3....1....3....1....3

%e ..2....3....2....3....1....2....1....1....2....1....1....2....3....1....2....2

%e ..3....1....1....1....2....1....3....2....3....3....3....1....1....2....3....3

%e ..1....3....3....2....3....2....2....1....1....2....2....2....2....1....1....1

%e ..2....2....1....1....1....3....3....2....3....1....3....1....3....3....3....3

%Y Row n=6 of A322013.

%K nonn

%O 0,4

%A _R. H. Hardin_, May 21 2011

%E a(0)=1 prepended by _Seiichi Manyama_, Nov 16 2018