A331923 Number of compositions (ordered partitions) of n into distinct perfect powers.

1, 1, 0, 0, 1, 2, 0, 0, 1, 3, 2, 0, 2, 8, 6, 0, 1, 4, 6, 0, 2, 12, 24, 0, 2, 9, 8, 1, 8, 32, 30, 2, 7, 10, 32, 8, 11, 44, 150, 30, 34, 40, 18, 26, 20, 68, 78, 126, 56, 169, 80, 30, 40, 116, 294, 144, 162, 226, 182, 128, 66, 338, 348, 752, 199, 1048

Offset

0,6

Links

Robert Israel, Table of n, a(n) for n = 0..2600

Index entries for sequences related to compositions

Example

a(17) = 4 because we have [16, 1], [9, 8], [8, 9] and [1, 16].

Maple

N:= 200: # for a(0)..a(N)
PP:= {1, seq(seq(b^i, i=2..floor(log[b](N))), b=2..floor(sqrt(N)))}:
G:= mul(1+t*x^p, p=PP):
F:= proc(n) local R, k, v;
  R:= normal(coeff(G, x, n));
  add(k!*coeff(R, t, k), k=1..degree(R, t))
end proc:
F(0):= 1:
map(F, [$0..N]); # Robert Israel, Feb 03 2020

Mathematica

M = 200;
PP = Join[{1}, Table[Table[b^i, {i, 2, Floor[Log[b, M]]}], {b, 2, Floor[ Sqrt[M]]}] // Flatten // Union];
G = Product[1 + t x^p, {p, PP}];
a[n_] := Module[{R, k, v}, R = SeriesCoefficient[G, {x, 0, n}]; Sum[k! SeriesCoefficient[R, {t, 0, k}], {k, 1, Exponent[R, t]}]];
a[0] = 1;
a /@ Range[0, M] (* Jean-François Alcover, Oct 25 2020, after Robert Israel *)

Crossrefs

Cf. A001597, A078635, A112345, A282500, A284171, A331844, A331845.

Sequence in context: A350529 A322279 A350365 * A342129 A292861 A292133

Adjacent sequences: A331920 A331921 A331922 * A331924 A331925 A331926

Keyword

nonn,look

Author

Ilya Gutkovskiy, Feb 01 2020

Status

approved