A183243 Number of permutations of 1..n+11 with each element displaced by at least 6.

1, 64, 6724, 250464, 8751552, 252813312, 6860776320, 178195229760, 4564491262444, 116967725946488, 3030418865421197, 79901439039073238, 2153387935521461560, 59484865107386246288

Offset: 1

Author

R. H. Hardin, Jan 03 2011

Keywords

• nonn
• more

Comments

a(n) equals the permanent of the (n+11) X (n+11) matrix with 0's along the main diagonal, the first 5 superdiagonals and subdiagonals, and 1's everywhere else. - John M. Campbell, Jul 09 2011

Examples

			Some permutations of 1-15 with minimum displacement 6:
(12,9,15,10,11,13,14,1,3,4,5,6,7,2,8) (10,9,11,14,12,13,15,1,3,4,2,6,5,7,8)
(8,12,15,10,11,13,14,1,2,3,4,6,7,5,9) (12,11,9,10,15,13,1,14,2,3,5,4,7,6,8)
(12,8,9,10,11,14,13,2,15,1,5,6,7,3,4) (12,8,11,10,15,13,1,14,2,3,4,6,7,5,9)
(8,11,9,10,12,13,14,1,15,2,3,5,6,4,7) (10,8,9,12,11,13,15,14,1,2,3,5,7,4,6)
(10,9,12,11,13,15,1,14,2,3,4,5,7,6,8) (8,15,11,10,12,13,14,1,2,3,4,5,6,7,9)
(12,10,9,11,15,13,14,2,3,4,5,1,6,8,7) (12,8,9,10,11,13,14,1,15,3,4,5,7,2,6)
(8,14,9,10,11,12,13,15,1,3,2,5,6,4,7) (10,9,11,12,13,14,1,2,15,4,5,6,3,7,8)
(12,9,15,10,11,13,14,2,3,1,4,6,5,8,7) (10,9,15,12,11,14,13,2,3,1,4,6,7,8,5)
(8,10,9,13,11,12,1,14,15,2,4,3,6,7,5) (12,10,9,13,11,15,14,1,2,4,3,5,6,7,8)
(10,8,9,11,13,12,15,14,2,1,4,3,5,7,6) (8,10,12,11,13,15,14,1,2,4,5,3,6,7,9)
		

Crossrefs

Column 6 of A183244.

Programs

Maple

with(LinearAlgebra): nmax:=10: for k from 1 to nmax do T:=Matrix(1..k+11,1..k+11,1); for i from 0 to 5 do for n from 1 to k+11-i do T[n,n+i]:=0 od: od: for j from 1 to 5 do for n from j+1 to k+11 do T[n,n-j]:= 0: od: od: a(k):= Permanent(T); od: seq(a(n),n=1..nmax); # Johannes W. Meijer, Jul 09 2011

Mathematica

a[n_] := Permanent[Table[If[Abs[i-j]<6, 0, 1], {i, 1, n+11}, {j, 1, n+11}] ]; Table[an = a[n]; Print["a(", n , ") = ", an]; an, {n, 1, 14}] (* Jean-François Alcover, Jan 07 2016 *)