A348124 Number of compositions of n where the smallest part is smaller than the number of parts.

0, 1, 3, 6, 13, 28, 59, 122, 248, 501, 1009, 2028, 4070, 8159, 16343, 32717, 65472, 130991, 262041, 524157, 1048410, 2096943, 4194043, 8388285, 16776819, 33553946, 67108270, 134217002, 268434568, 536869825, 1073740493, 2147482019, 4294965305, 8589932164

Offset: 1

Author

R. J. Mathar, Oct 01 2021

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A011782, A098132, A098133.

Programs

Maple

b:= proc(n, s, c) option remember; `if`(s b(n$2, 0):
seq(a(n), n=1..40);  # Alois P. Heinz, Oct 01 2021

Mathematica

b[n_, s_, c_] := b[n, s, c] = If[s < c, Ceiling[2^(n - 1)],
     If[n == 0, 0, Sum[b[n - j, Min[j, s], c + 1], {j, 1, n}]]];
a[n_] := b[n, n, 0];
Table[a[n], {n, 1, 40}] (* Jean-François Alcover, Apr 14 2022, after Alois P. Heinz *)

Formula

a(n) + A098132(n) + A098133(n) = 2^(n-1).

Extensions

a(23)-a(34) from Alois P. Heinz, Oct 01 2021