A347586 Number of partitions of n into at most 4 distinct parts.

1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 12, 15, 18, 22, 26, 31, 36, 43, 49, 57, 65, 75, 84, 96, 107, 121, 134, 150, 165, 184, 201, 222, 242, 266, 288, 315, 340, 370, 398, 431, 462, 499, 533, 573, 611, 655, 696, 744, 789, 841, 890, 946, 999, 1060, 1117, 1182, 1244, 1314, 1380, 1455

Offset

0,4

Links

Table of n, a(n) for n=0..60.

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

Formula

G.f.: Sum_{k=0..4} x^(k*(k + 1)/2) / Product_{j=1..k} (1 - x^j).

a(n) ~ A000578(n)/144. - Stefano Spezia, Sep 08 2021

Mathematica

nmax = 60; CoefficientList[Series[Sum[x^(k (k + 1)/2)/Product[(1 - x^j), {j, 1, k}], {k, 0, 4}], {x, 0, nmax}], x]
Join[{1}, LinearRecurrence[{1, 1, 0, 0, -2, 0, 0, 1, 1, -1}, {1, 1, 2, 2, 3, 4, 5, 6, 8, 10}, 60]]

Crossrefs

Cf. A000578, A001400, A014591, A065033, A347587, A347588.

Sequence in context: A034143 A309999 A034144 * A287997 A352165 A034145

Adjacent sequences: A347583 A347584 A347585 * A347587 A347588 A347589

Keyword

nonn,easy

Author

Ilya Gutkovskiy, Sep 08 2021

Status

approved