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%I #22 Jan 13 2022 01:35:12
%S 1,64,6724,250464,8751552,252813312,6860776320,178195229760,
%T 4564491262444,116967725946488,3030418865421197,79901439039073238,
%U 2153387935521461560,59484865107386246288
%N Number of permutations of 1..n+11 with each element displaced by at least 6.
%C 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
%e Some permutations of 1-15 with minimum displacement 6:
%e (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)
%e (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)
%e (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)
%e (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)
%e (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)
%e (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)
%e (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)
%e (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)
%e (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)
%e (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)
%p 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
%t 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 *)
%Y Column 6 of A183244.
%K nonn,more
%O 1,2
%A _R. H. Hardin_, Jan 03 2011
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