A244714 Number of compositions of n with exactly 2 transitions between different parts.

1, 4, 14, 29, 56, 100, 148, 230, 322, 446, 573, 778, 953, 1215, 1456, 1806, 2134, 2542, 2944, 3477, 3968, 4600, 5186, 5872, 6657, 7446, 8304, 9217, 10258, 11172, 12465, 13564, 14867, 16072, 17716, 18816, 20832, 22055, 24144, 25504, 27904, 29168, 32051, 33375

Offset

4,2

Links

Alois P. Heinz, Table of n, a(n) for n = 4..1000

Example

a(4) = 1: [1,2,1].
a(5) = 4: [1,1,2,1], [1,2,1,1], [1,3,1], [2,1,2].

Maple

b:= proc(n, v) option remember; `if`(n=0, [1, 0$2],
      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..2][]]), i=1..n))
    end:
a:= n-> b(n, 0)[3]:
seq(a(n), n=4..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, 2];
Table[a[n], {n, 4, 60}] (* Jean-François Alcover, Aug 29 2021, after A238279 Maple code *)

Crossrefs

Column k=2 of A238279.

Sequence in context: A316213 A296985 A338311 * A218212 A305637 A103779

Adjacent sequences: A244711 A244712 A244713 * A244715 A244716 A244717

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jul 04 2014

Status

approved