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%I #19 Mar 08 2020 00:05:46
%S 1,1,2,1,4,9,1,8,29,44,1,16,112,206,265,1,32,436,1168,1708,1854,1,64,
%T 1708,6984,13365,15702,14833,1,128,6724,41808,114124,159414,159737,
%U 133496,1,256,26572,250464,998112,1799688,2036488,1780696,1334961,1,512
%N T(n,k) = Number of permutations of 1..n+2*k-1 with each element displaced by at least k.
%C Table starts
%C ........1.........1..........1............1.............1...............1
%C ........2.........4..........8...........16............32..............64
%C ........9........29........112..........436..........1708............6724
%C .......44.......206.......1168.........6984.........41808..........250464
%C ......265......1708......13365.......114124........998112.........8751552
%C .....1854.....15702.....159414......1799688......21201024.......252813312
%C ....14833....159737....2036488.....29125117.....441629332......6860776320
%C ...133496...1780696...27780408....486980182....9154333160....178195229760
%C ..1334961..21599745..404351752...8490078104..192565379941...4564491262444
%C .14684570.283294740.6263006598.154750897552.4146526612518.116967725946488
%H R. H. Hardin, <a href="/A183244/b183244.txt">Table of n, a(n) for n = 1..201</a>
%e All permutations of 1-5 with minimum displacement 2:
%e (3,4,5,1,2) (3,4,5,2,1) (4,5,1,2,3) (5,4,1,2,3).
%t T[n_, k_] := Permanent[nrows = n+2k-1; Table[If[Abs[i-j] <= k-1, 0, 1], {i, 1, nrows}, {j, 1, nrows}]]; Table[t = T[n-k+1, k]; Print[ "T(", n-k+1, ",", k, ") = ", t]; t, {n, 1, 9}, {k, n, 1, -1}] // Flatten (* _Jean-François Alcover_, Jan 07 2016, adapted from Sage *)
%o (Sage)
%o def A183244_T(n,k):
%o return Matrix(lambda i,j: 0 if abs(i-j) <= (k-1) else 1, nrows=n+2*k-1).permanent() # _D. S. McNeil_, Jan 04 2011
%Y Column 1 is A000166(n+1).
%Y Column 2 is A001883(n+3).
%Y Column 3 is A075851(n+5).
%Y Column 4 is A075852(n+7).
%K nonn,tabl
%O 1,3
%A _R. H. Hardin_, Jan 03 2011
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