login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A342229 Total sum of parts which are cubes in all partitions of n. 1
0, 1, 2, 4, 7, 12, 19, 30, 53, 75, 113, 163, 235, 328, 461, 628, 868, 1163, 1564, 2069, 2743, 3578, 4674, 6036, 7795, 9962, 12728, 16151, 20441, 25714, 32290, 40332, 50292, 62405, 77288, 95339, 117382, 143987, 176298, 215168, 262121, 318385, 386043, 466838, 563577, 678712 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..45.

FORMULA

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

a(n) = Sum_{k=1..n} A113061(k) * A000041(n-k).

EXAMPLE

For n = 4 we have:

--------------------------------

Partitions        Sum of parts

.               which are cubes

--------------------------------

4 ................... 0

3 + 1 ............... 1

2 + 2 ............... 0

2 + 1 + 1 ........... 2

1 + 1 + 1 + 1 ....... 4

--------------------------------

Total ............... 7

So a(4) = 7.

MATHEMATICA

nmax = 45; CoefficientList[Series[Sum[k^3 x^(k^3)/(1 - x^(k^3)), {k, 1, Floor[nmax^(1/3)] + 1}]/Product[(1 - x^j), {j, 1, nmax}], {x, 0, nmax}], x]

Table[Sum[DivisorSum[k, # &, IntegerQ[#^(1/3)] &] PartitionsP[n - k], {k, 1, n}], {n, 0, 45}]

CROSSREFS

Cf. A000041, A000578, A066186, A113061, A264392, A342228.

Sequence in context: A102346 A333148 A343661 * A326080 A287525 A244472

Adjacent sequences:  A342226 A342227 A342228 * A342230 A342231 A342232

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Mar 06 2021

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 17 17:29 EDT 2021. Contains 347489 sequences. (Running on oeis4.)