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A335942 Number of compositions of n such that the set s of parts and multiplicities satisfies s = {1..max(s)}. 4
1, 1, 2, 2, 3, 12, 12, 32, 51, 144, 191, 486, 679, 1487, 3149, 5909, 11637, 18630, 36928, 76431, 141009, 264784, 535057, 921105, 1774022, 3388054, 6303519, 12255373, 22527578, 43358822, 77695383, 145170435, 264722429, 527776034, 936538336, 1807344134 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Chai Wah Wu, Table of n, a(n) for n = 0..142 (n = 0..100 from Alois P. Heinz)

EXAMPLE

a(4) = 3: 211, 121, 112.

a(5) = 12: 23, 32, 113, 122, 131, 212, 221, 311, 1112, 1121, 1211, 2111.

MAPLE

b:= proc(n, i, s, p) option remember;

     `if`(n=0, `if`(s={$0..max(s)}, p!, 0), `if`(i<1, 0, add(

      b(n-i*j, i-1, {s[], j, `if`(j=0, 0, i)}, p+j)/j!, j=0..n/i)))

    end:

a:= n-> b(n, floor((sqrt(1+8*(n+1))-1)/2), {0}, 0):

seq(a(n), n=0..35);

MATHEMATICA

b[n_, i_, s_, p_] := b[n, i, s, p] =

     If[n == 0, If[s == Range[0, Max[s]], p!, 0], If[i < 1, 0, Sum[

     b[n - i*j, i - 1, Union@Flatten@{s, j, If[j == 0, 0, i]}, p + j]/j!,

     {j, 0, n/i}]]];

a[n_] := b[n, Floor[(Sqrt[1 + 8*(n + 1)] - 1)/2], {0}, 0];

Table[a[n], {n, 0, 35}] (* Jean-Fran├žois Alcover, May 30 2022, after Alois P. Heinz *)

CROSSREFS

Cf. A107429, A329741, A335941.

Sequence in context: A134243 A182779 A199673 * A240133 A293445 A126339

Adjacent sequences:  A335939 A335940 A335941 * A335943 A335944 A335945

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jun 30 2020

STATUS

approved

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Last modified August 9 21:08 EDT 2022. Contains 356026 sequences. (Running on oeis4.)