A244717 Number of compositions of n with exactly 5 transitions between different parts.

2, 16, 78, 274, 814, 2058, 4752, 9930, 19574, 36186, 63924, 108078, 176672, 279260, 429800, 645222, 947142, 1363678, 1927532, 2681804, 3673786, 4967774, 6630024, 8752102, 11422254, 14770528, 18913112, 24022400, 30253734, 37831400, 46953628, 57914360, 70960394

Offset

9,1

Links

Alois P. Heinz, Table of n, a(n) for n = 9..900

Maple

b:= proc(n, v) option remember; `if`(n=0, [1, 0$5],
      add(`if`(v in [0, i], b(n-i, `if`(i<=n-i, i, -1)),
      [0, b(n-i, `if`(i<=n-i, i, -1))[1..5][]]), i=1..n))
    end:
a:= n-> b(n, 0)[6]:
seq(a(n), n=9..60);

Mathematica

b[n_, v_] := b[n, v] = If[n == 0, 1, Expand[Sum[b[n - i, i]*
     If[v == 0 || v == i, 1, x], {i, n}]]];
a[n_] := Coefficient[b[n, 0], x, 5];
Table[a[n], {n, 9, 60}] (* Jean-François Alcover, Aug 29 2021, after A238279 Maple code *)

Crossrefs

Column k=5 of A238279.

Sequence in context: A034581 A356372 A028336 * A208102 A207723 A208835

Adjacent sequences: A244714 A244715 A244716 * A244718 A244719 A244720

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jul 04 2014

Status

approved