A347588 Number of partitions of n into at most 6 distinct parts.

1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 12, 15, 18, 22, 27, 32, 38, 46, 54, 64, 76, 89, 104, 122, 142, 165, 192, 221, 255, 294, 337, 385, 441, 501, 570, 646, 731, 824, 930, 1043, 1171, 1310, 1464, 1630, 1817, 2015, 2236, 2473, 2734, 3013, 3322, 3648, 4008, 4391, 4809, 5252, 5738, 6249

Offset: 0

Author

Ilya Gutkovskiy, Sep 08 2021

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (1,1,0,0,-1,0,-2,0,1,1,1,1,0,-2,0,-1,0,0,1,1,-1).

Crossrefs

Cf. A001402, A014591, A065033, A347586, A347587.

Programs

Mathematica

nmax = 58; CoefficientList[Series[Sum[x^(k (k + 1)/2)/Product[(1 - x^j), {j, 1, k}], {k, 0, 6}], {x, 0, nmax}], x]
Join[{1}, LinearRecurrence[{1, 1, 0, 0, -1, 0, -2, 0, 1, 1, 1, 1, 0, -2, 0, -1, 0, 0, 1, 1, -1}, {1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 12, 15, 18, 22, 27, 32, 38, 46, 54, 64, 76}, 58]]

Formula

G.f.: Sum_{k=0..6} x^(k*(k + 1)/2) / Product_{j=1..k} (1 - x^j).