A336875 Number of parts, counted without multiplicity, in all compositions of n.

0, 1, 2, 6, 13, 30, 66, 144, 308, 655, 1380, 2891, 6024, 12500, 25844, 53274, 109530, 224690, 460033, 940276, 1918979, 3911186, 7962194, 16191875, 32896364, 66776727, 135445212, 274532607, 556086916, 1125727954, 2277650681, 4605981879, 9310120876, 18810538092

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Example

a(4) = 1 + 2 + 2 + 2 + 1 + 2 + 2 + 1 = 13: (1)111, (1)1(2), (1)(2)1, (2)(1)1, (2)2, (1)(3), (3)(1), (4).

Maple

b:= proc(n, i, p) option remember; `if`(n=0, [p!, 0],
      `if`(i<1, 0, add((p-> [0, `if`(j=0, 0, p[1])]+p)(
         b(n-i*j, i-1, p+j)/j!), j=0..n/i)))
    end:
a:= n-> b(n$2, 0)[2]:
seq(a(n), n=0..38);

Mathematica

b[n_, i_, p_] := b[n, i, p] = If[n == 0, {p!, 0},
     If[i<1, {0, 0}, Sum[{0, If[j == 0, 0, #[[1]]]}+#&[
     b[n-i*j, i-1, p+j]/j!], {j, 0, n/i}]]];
a[n_] := b[n, n, 0][[2]];
a /@ Range[0, 38] (* Jean-François Alcover, Jun 13 2021, after Alois P. Heinz *)

Crossrefs

Cf. A000070 (the same for partitions), A001792 (all parts), A097910, A336516.

Sequence in context: A115217 A094687 A369584 * A219753 A239305 A018013

Adjacent sequences: A336872 A336873 A336874 * A336876 A336877 A336878

Keyword

nonn

Author

Alois P. Heinz, Aug 06 2020

Status

approved