A336273 Number of compositions of n containing at least one part p of multiplicity p.

0, 1, 0, 2, 3, 5, 14, 28, 44, 101, 207, 399, 779, 1609, 3122, 6121, 11804, 23631, 46273, 91604, 178096, 352419, 691996, 1371306, 2702206, 5356324, 10604748, 21080216, 41869930, 83383786, 166114046, 331434088, 661685588, 1322042390, 2642367028, 5283397304

Offset

0,4

Links

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

Formula

a(n) = A011782(n) - A336269(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-> ceil(2^(n-1))-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_] := Ceiling[2^(n - 1)] - b[n, n, 0];
Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Apr 14 2022, after Alois P. Heinz *)

Crossrefs

Cf. A011782, A336269.

Sequence in context: A283448 A177901 A143743 * A104870 A232162 A243555

Adjacent sequences: A336270 A336271 A336272 * A336274 A336275 A336276

Keyword

nonn

Author

Alois P. Heinz, Jul 15 2020

Status

approved