A336269 Number of compositions of n containing no part p of multiplicity p.

1, 0, 2, 2, 5, 11, 18, 36, 84, 155, 305, 625, 1269, 2487, 5070, 10263, 20964, 41905, 84799, 170540, 346192, 696157, 1405156, 2822998, 5686402, 11420892, 22949684, 46028648, 92347798, 185051670, 370756866, 742307736, 1485798060, 2972924906, 5947567564

Offset

0,3

Links

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

Formula

a(n) = A011782(n) - A336273(n).

Maple

b:= proc(n, i, p) option remember; `if`(n=0, p!, `if`(i<1, 0,
      add(`if`(i=j, 0, b(n-i*j, i-1, p+j)/j!), j=0..n/i)))
    end:
a:= n-> b(n$2, 0):
seq(a(n), n=0..40);

Mathematica

b[n_, i_, p_] := b[n, i, p] = If[n == 0, p!, If[i < 1, 0,
     Sum[If[i == j, 0, b[n - i*j, i - 1, p + j]/j!], {j, 0, n/i}]]];
a[n_] := b[n, n, 0];
Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Mar 17 2022, after Alois P. Heinz *)

Crossrefs

Cf. A011782, A242434, A276429, A336273.

Sequence in context: A259828 A366094 A104080 * A078405 A109278 A367966

Adjacent sequences: A336266 A336267 A336268 * A336270 A336271 A336272

Keyword

nonn

Author

Alois P. Heinz, Jul 15 2020

Status

approved