A339102 Number of compositions (ordered partitions) of n into distinct parts >= 4.

1, 0, 0, 0, 1, 1, 1, 1, 1, 3, 3, 5, 5, 7, 7, 15, 15, 23, 29, 37, 43, 57, 87, 101, 137, 175, 235, 279, 363, 431, 665, 757, 1015, 1257, 1683, 2069, 2645, 3199, 4063, 5607, 6759, 8591, 10877, 13837, 17251, 22185, 26871, 33773, 41273, 56047, 66499, 85647, 104811

Offset

0,10

Links

Table of n, a(n) for n=0..52.

Index entries for sequences related to compositions

Formula

G.f.: Sum_{k>=0} k! * x^(k*(k + 7)/2) / Product_{j=1..k} (1 - x^j).

Example

a(9) = 3 because we have [9], [5, 4] and [4, 5].

Maple

b:= proc(n, i, p) option remember;
      `if`(n=0, p!, `if`((i-3)*(i+4)/2<n, 0,
       add(b(n-i*j, i-1, p+j), j=0..min(1, n/i))))
    end:
a:= n-> b(n$2, 0):
seq(a(n), n=0..60);  # Alois P. Heinz, Nov 23 2020

Mathematica

nmax = 52; CoefficientList[Series[Sum[k! x^(k (k + 7)/2)/Product[1 - x^j, {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A008484, A017898, A025149, A032020, A032022, A339101, A339103, A339104.

Sequence in context: A111213 A333153 A245146 * A095878 A341143 A369337

Adjacent sequences: A339099 A339100 A339101 * A339103 A339104 A339105

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 23 2020

Status

approved