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A331923 Number of compositions (ordered partitions) of n into distinct perfect powers. 1
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Oct 25 2020, after Robert Israel *)

CROSSREFS

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

Sequence in context: A217315 A217593 A322279 * A342129 A292861 A292133

Adjacent sequences:  A331920 A331921 A331922 * A331924 A331925 A331926

KEYWORD

nonn,look

AUTHOR

Ilya Gutkovskiy, Feb 01 2020

STATUS

approved

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Last modified September 27 19:34 EDT 2021. Contains 347694 sequences. (Running on oeis4.)