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

1,3

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

Links

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

Example

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).

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 *)

Prog

(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

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).

Sequence in context: A359132 A076014 A120458 * A086933 A077878 A128058

Adjacent sequences: A183241 A183242 A183243 * A183245 A183246 A183247

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 03 2011

Status

approved