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

Author

Joerg Arndt and Alois P. Heinz, Jul 04 2014

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Column k=2 of A238279.

Programs

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 *)