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A183244 T(n,k) = Number of permutations of 1..n+2*k-1 with each element displaced by at least k. 8
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 (list; table; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 03 2011
STATUS
approved

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Last modified July 19 17:03 EDT 2024. Contains 374410 sequences. (Running on oeis4.)