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

0,4

Links

Table of n, a(n) for n=0..58.

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).

Formula

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

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]]

Crossrefs

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

Sequence in context: A034321 A034320 A058703 * A000009 A081360 A117409

Adjacent sequences: A347585 A347586 A347587 * A347589 A347590 A347591

Keyword

nonn,easy

Author

Ilya Gutkovskiy, Sep 08 2021

Status

approved