A183244 T(n,k) = Number of permutations of 1..n+2*k-1 with each element displaced by at least k.

1, 1, 2, 1, 4, 9, 1, 8, 29, 44, 1, 16, 112, 206, 265, 1, 32, 436, 1168, 1708, 1854, 1, 64, 1708, 6984, 13365, 15702, 14833, 1, 128, 6724, 41808, 114124, 159414, 159737, 133496, 1, 256, 26572, 250464, 998112, 1799688, 2036488, 1780696, 1334961, 1, 512

Offset: 1

Author

R. H. Hardin, Jan 03 2011

Keywords

• nonn
• tabl

Comments

Table starts

........1.........1..........1............1.............1...............1

........2.........4..........8...........16............32..............64

........9........29........112..........436..........1708............6724

.......44.......206.......1168.........6984.........41808..........250464

......265......1708......13365.......114124........998112.........8751552

.....1854.....15702.....159414......1799688......21201024.......252813312

....14833....159737....2036488.....29125117.....441629332......6860776320

...133496...1780696...27780408....486980182....9154333160....178195229760

..1334961..21599745..404351752...8490078104..192565379941...4564491262444

.14684570.283294740.6263006598.154750897552.4146526612518.116967725946488

Examples

			All permutations of 1-5 with minimum displacement 2:
(3,4,5,1,2) (3,4,5,2,1) (4,5,1,2,3) (5,4,1,2,3).
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..201

Crossrefs

Column 1 is A000166(n+1).

Column 2 is A001883(n+3).

Column 3 is A075851(n+5).

Column 4 is A075852(n+7).

Programs

Mathematica

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 *)

Sage

def A183244_T(n,k):
    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