A000467 Number of permutations of [n] in which the longest increasing run has length 6. (Formerly M4868 N2083)

0, 0, 0, 0, 0, 1, 12, 137, 1602, 19710, 257400, 3574957, 52785901, 827242933, 13730434111, 240806565782, 4452251786946, 86585391630673, 1767406549387381, 37790452850585180, 844817788372455779, 19711244788916894489, 479203883157602851294

Offset

1,7

References

F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 261.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Alois P. Heinz, Table of n, a(n) for n = 1..450 (first 100 terms from Max Alekseyev)

Max A. Alekseyev, On the number of permutations with bounded run lengths, arXiv preprint arXiv:1205.4581 [math.CO], 2012.

Mathematica

b[u_, o_, t_, k_] := b[u, o, t, k] = If[t == k, (u + o)!, If[Max[t, u] + o < k, 0, Sum[b[u + j - 1, o - j, t + 1, k], {j, 1, o}] + Sum[b[u - j, o + j - 1, 1, k], {j, 1, u}]]]; T[n_, k_] := b[0, n, 0, k] - b[0, n, 0, k + 1]; a[n_] := T[n, 6]; Array[a, 23] (* Jean-François Alcover, Feb 08 2016, after Alois P. Heinz in A008304 *)

Crossrefs

Column 6 of A008304. Other columns: A000303, A000402, A000434, A000456.

Cf. A001250, A001251, A001252, A001253, A010026, A211318.

Sequence in context: A351514 A216081 A264503 * A059517 A243966 A097167

Adjacent sequences: A000464 A000465 A000466 * A000468 A000469 A000470

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Edited and extended by Max Alekseyev, May 20 2012

Status

approved