A230055 Number of permutations of [n] in which the longest increasing run has length 7.

1, 14, 181, 2360, 32010, 456720, 6881160, 109546009, 1841298059, 32629877967, 608572228291, 11923667699474, 244964063143590, 5267496652725480, 118348438201424761, 2773714509551524351, 67705791536824698266, 1718769199589362743761, 45314525515737783596251

Offset

7,2

Links

Alois P. Heinz, Table of n, a(n) for n = 7..200

Formula

a(n) = A230051(n) - A177553(n).

E.g.f.: 1/Sum_{n>=0} (8*n+1-x)*x^(8*n)/(8*n+1)! - 1/Sum_{n>=0} (7*n+1-x)*x^(7*n)/(7*n+1)!.

Example

a(7) = 1: 1234567.
a(8) = 14: 12345687, 12345786, 12346785, 12356784, 12456783, 13456782, 21345678, 23456781, 31245678, 41235678, 51234678, 61234578, 71234568, 81234567.

Maple

b:= proc(u, o, t, k) option remember; `if`(u+o=0, 1,
      `if`(t<k-1, add(b(u+j-1, o-j, t+1, k), j=1..o), 0)+
      add(b(u-j, o+j-1, 0, k), j=1..u))
    end:
a:= n-> b(n, 0, 0, 7)-b(n, 0, 0, 6):
seq(a(n), n=7..30);

Mathematica

b[u_, o_, t_, k_] := b[u, o, t, k] = If[u + o == 0, 1, If[t < k - 1, Sum[b[u + j - 1, o - j, t + 1, k], {j, 1, o}], 0] + Sum[b[u - j, o + j - 1, 0, k], {j, 1, u}]];
a[n_] := b[n, 0, 0, 7] - b[n, 0, 0, 6];
Table[a[n], {n, 7, 30}] (* Jean-François Alcover, Jul 19 2018, after Alois P. Heinz *)

Crossrefs

Column k=7 of A008304.

Sequence in context: A125471 A132010 A126866 * A133286 A163416 A162783

Adjacent sequences: A230052 A230053 A230054 * A230056 A230057 A230058

Keyword

nonn

Author

Alois P. Heinz, Oct 07 2013

Status

approved