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A276974 Number T(n,k) of permutations of [n] where the minimal distance between elements of the same cycle equals k (k=n for the identity permutation in S_n); triangle T(n,k), n>=0, 0<=k<=n, read by rows. 4
1, 0, 1, 0, 1, 1, 0, 4, 1, 1, 0, 19, 3, 1, 1, 0, 103, 12, 3, 1, 1, 0, 651, 54, 10, 3, 1, 1, 0, 4702, 281, 42, 10, 3, 1, 1, 0, 38413, 1652, 203, 37, 10, 3, 1, 1, 0, 350559, 11017, 1086, 166, 37, 10, 3, 1, 1, 0, 3539511, 81665, 6564, 857, 151, 37, 10, 3, 1, 1, 0, 39196758, 669948, 44265, 4900, 726, 151, 37, 10, 3, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

LINKS

Alois P. Heinz, Rows n = 0..12, flattened

Per Alexandersson et al., d-regular partitions and permutations, MathOverflow, 2014

EXAMPLE

T(3,1) = 4: (1,2,3), (1,3,2), (1)(2,3), (1,2)(3).

T(3,2) = 1: (1,3)(2).

T(3,3) = 1: (1)(2)(3).

Triangle T(n,k) begins:

  1;

  0,       1;

  0,       1,     1;

  0,       4,     1,    1;

  0,      19,     3,    1,   1;

  0,     103,    12,    3,   1,   1;

  0,     651,    54,   10,   3,   1,  1;

  0,    4702,   281,   42,  10,   3,  1,  1;

  0,   38413,  1652,  203,  37,  10,  3,  1, 1;

  0,  350559, 11017, 1086, 166,  37, 10,  3, 1, 1;

  0, 3539511, 81665, 6564, 857, 151, 37, 10, 3, 1, 1;

  ...

CROSSREFS

Columns k=0-1 give: A000007, A276975.

Row sums give A000142.

T(2n,n) = A138378(n) = A005493(n-1) for n>0.

Cf. A239145, A263757, A277031.

Sequence in context: A276834 A016684 A324564 * A122777 A103524 A110916

Adjacent sequences:  A276971 A276972 A276973 * A276975 A276976 A276977

KEYWORD

nonn,tabl

AUTHOR

Alois P. Heinz, Sep 23 2016

STATUS

approved

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Last modified June 19 17:25 EDT 2021. Contains 345144 sequences. (Running on oeis4.)