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A242434 Number of compositions of n in which each part p has multiplicity p. 3
1, 1, 0, 0, 1, 3, 0, 0, 0, 1, 4, 0, 0, 10, 60, 0, 1, 5, 0, 0, 15, 105, 0, 0, 0, 36, 286, 0, 0, 1281, 12768, 0, 0, 0, 56, 504, 1, 7, 2520, 27720, 28, 378, 1260, 0, 0, 7014, 84000, 0, 0, 4621, 83168, 360360, 210, 2346, 2522880, 37837800, 13860, 180180, 120, 1320 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

a(n) = 0 for n in {A001422}, a(n) > 0 for n in {A003995}.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..4500

EXAMPLE

a(0) = 1: the empty composition.

a(1) = 1: [1].

a(4) = 1: [2,2].

a(5) = 3: [1,2,2], [2,1,2], [2,2,1].

a(9) = 1: [3,3,3].

a(10) = 4: [1,3,3,3], [3,1,3,3], [3,3,1,3], [3,3,3,1].

a(13) = 10: [2,2,3,3,3], [2,3,2,3,3], [2,3,3,2,3], [2,3,3,3,2], [3,2,2,3,3], [3,2,3,2,3], [3,2,3,3,2], [3,3,2,2,3], [3,3,2,3,2], [3,3,3,2,2].

MAPLE

b:= proc(n, i, p) option remember; `if`(n=0, p!, `if`(i<1, 0,

       b(n, i-1, p) +`if`(i^2>n, 0, b(n-i^2, i-1, p+i)/i!)))

    end:

a:= n-> b(n, isqrt(n), 0):

seq(a(n), n=0..100);

MATHEMATICA

b[n_, i_, p_] := b[n, i, p] = If[n==0, p!, If[i<1, 0, b[n, i-1, p] + If[i^2 >n, 0, b[n-i^2, i-1, p+i]/i!]]]; a[n_] := b[n, Floor[Sqrt[n]], 0]; Table[ a[n], {n, 0, 100}] (* Jean-Fran├žois Alcover, Feb 08 2017, translated from Maple *)

CROSSREFS

Cf. A033461 (the same for partitions), A336269.

Sequence in context: A328969 A027185 A035641 * A036873 A081130 A174428

Adjacent sequences:  A242431 A242432 A242433 * A242435 A242436 A242437

KEYWORD

nonn,look

AUTHOR

Alois P. Heinz, May 14 2014

STATUS

approved

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Last modified September 24 11:11 EDT 2020. Contains 337317 sequences. (Running on oeis4.)