A347548 Number of partitions of n into 3 or more distinct parts.

1, 1, 2, 3, 5, 6, 9, 11, 15, 19, 24, 29, 37, 44, 54, 65, 78, 92, 110, 129, 152, 178, 208, 241, 281, 324, 374, 431, 495, 567, 650, 741, 845, 962, 1093, 1239, 1405, 1588, 1794, 2025, 2281, 2566, 2886, 3239, 3633, 4071, 4556, 5093, 5691, 6350, 7080, 7888, 8779, 9762, 10850

Offset

6,3

Links

Table of n, a(n) for n=6..60.

Formula

G.f.: Sum_{k>=3} x^(k*(k + 1)/2) / Product_{j=1..k} (1 - x^j).

a(n) = A000009(n) - floor((n + 1)/2). - Vaclav Kotesovec, Sep 14 2021

Mathematica

nmax = 60; CoefficientList[Series[Sum[x^(k (k + 1)/2)/Product[(1 - x^j), {j, 1, k}], {k, 3, nmax}], {x, 0, nmax}], x] // Drop[#, 6] &

Crossrefs

Cf. A000009, A004526, A111133, A347549.

Sequence in context: A309831 A309830 A008770 * A230515 A030068 A239958

Adjacent sequences: A347545 A347546 A347547 * A347549 A347550 A347551

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 06 2021

Status

approved