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

1,2

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

Links

Table of n, a(n) for n=1..14.

Example

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)

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 *)

Crossrefs

Column 6 of A183244.

Sequence in context: A349506 A264188 A333583 * A264075 A223198 A281836

Adjacent sequences: A183240 A183241 A183242 * A183244 A183245 A183246

Keyword

nonn,more

Author

R. H. Hardin, Jan 03 2011

Status

approved