A244716 Number of compositions of n with exactly 4 transitions between different parts.

1, 6, 31, 99, 278, 654, 1390, 2714, 4927, 8531, 13963, 22134, 33767, 50283, 72470, 102891, 142375, 194202, 260093, 343973, 447906, 577636, 735540, 928009, 1159312, 1436145, 1765079, 2152787, 2608321, 3137866, 3755214, 4464420, 5284570, 6216275, 7287298, 8494233

Offset

7,2

Links

Alois P. Heinz, Table of n, a(n) for n = 7..900

Maple

b:= proc(n, v) option remember; `if`(n=0, [1, 0$4],
      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..4][]]), i=1..n))
    end:
a:= n-> b(n, 0)[5]:
seq(a(n), n=7..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, 4];
Table[a[n], {n, 7, 60}] (* Jean-François Alcover, Aug 29 2021, after A238279 Maple code *)

Crossrefs

Column k=4 of A238279.

Sequence in context: A273790 A096959 A112562 * A024447 A303172 A354552

Adjacent sequences: A244713 A244714 A244715 * A244717 A244718 A244719

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jul 04 2014

Status

approved