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!)
A339420 Number of compositions (ordered partitions) of n into an even number of cubes. 2
1, 0, 1, 0, 1, 0, 1, 0, 1, 2, 1, 4, 1, 6, 1, 8, 2, 10, 7, 12, 16, 14, 29, 16, 46, 22, 67, 40, 94, 78, 125, 144, 161, 246, 214, 394, 312, 602, 499, 878, 835, 1236, 1396, 1722, 2286, 2446, 3637, 3614, 5598, 5560, 8358, 8782, 12226, 14014, 17776, 22278, 26056, 34924 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,10

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..5000

Index entries for sequences related to compositions

Index entries for sequences related to sums of cubes

FORMULA

G.f.: (1/2) * (1 / (1 - Sum_{k>=1} x^(k^3)) + 1 / Sum_{k>=0} x^(k^3)).

a(n) = (A023358(n) + A323633(n)) / 2.

a(n) = Sum_{k=0..n} A023358(k) * A323633(n-k).

EXAMPLE

a(11) = 4 because we have [8, 1, 1, 1], [1, 8, 1, 1], [1, 1, 8, 1] and [1, 1, 1, 8].

MAPLE

b:= proc(n, t) option remember; local r, f, g;

      if n=0 then t else r, f, g:=$0..2; while f<=n

      do r, f, g:= r+b(n-f, 1-t), f+3*g*(g-1)+1, g+1 od; r fi

    end:

a:= n-> b(n, 1):

seq(a(n), n=0..60);  # Alois P. Heinz, Dec 03 2020

MATHEMATICA

nmax = 57; CoefficientList[Series[(1/2) (1/(1 - Sum[x^(k^3), {k, 1, Floor[nmax^(1/3)] + 1}]) + 1/Sum[x^(k^3), {k, 0, Floor[nmax^(1/3)] + 1}]), {x, 0, nmax}], x]

CROSSREFS

Cf. A000578, A023358, A034008, A323633, A339368, A339418, A339421.

Sequence in context: A327529 A318775 A317500 * A317494 A317505 A137374

Adjacent sequences:  A339417 A339418 A339419 * A339421 A339422 A339423

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Dec 03 2020

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 27 04:10 EDT 2021. Contains 347673 sequences. (Running on oeis4.)