A244715 Number of compositions of n with exactly 3 transitions between different parts.

2, 10, 36, 86, 200, 374, 680, 1122, 1796, 2694, 3954, 5600, 7752, 10448, 13798, 18072, 23032, 29218, 36390, 45044, 54870, 66852, 79790, 95550, 112662, 132938, 154752, 180614, 207764, 239784, 273898, 312922, 354240, 401826, 451598, 508134, 567756, 634634, 705506

Offset: 6

Author

Joerg Arndt and Alois P. Heinz, Jul 04 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 6..900

Crossrefs

Column k=3 of A238279.

Programs

Maple

b:= proc(n, v) option remember; `if`(n=0, [1, 0$3],
      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..3][]]), i=1..n))
    end:
a:= n-> b(n, 0)[4]:
seq(a(n), n=6..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, 3];
Table[a[n], {n, 6, 60}] (* Jean-François Alcover, Aug 29 2021, after A238279 Maple code *)