A340980 -id:A340980 - cp's OEIS frontend

A051344 Number of ways of writing n as a sum of 3 positive cubes (counted naively).

0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6

Offset: 0

N. J. A. Sloane

Seiichi Manyama, Table of n, a(n) for n = 0..10000
Index entries for sequences related to sums of cubes

Cf. A280618, A340977, A340978, A340979, A340980, A340981, A340982, A340983.

Cf. A051343.

Maple
```
series(add(x^(n^3), n=1..10)^3,x,1000);
```

A340977 Number of ways to write n as an ordered sum of 4 positive cubes.

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 1, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 4, 0, 0, 6, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 12, 4, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 24

Offset: 4

Ilya Gutkovskiy, Feb 01 2021

nonn

Robert Israel, Table of n, a(n) for n = 4..10000
Index entries for sequences related to sums of cubes

Cf. A000578, A010057, A025457, A051344, A173678, A280618, A340978, A340979, A340980, A340981, A340982, A340983.

b:= proc(n, t) option remember;
      `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add((s->
      `if`(s>n, 0, b(n-s, t-1)))(j^3), j=1..iroot(n, 3))))
    end:
a:= n-> b(n, 4):
seq(a(n), n=4..100);  # Alois P. Heinz, Feb 01 2021

nmax = 100; CoefficientList[Series[Sum[x^(k^3), {k, 1, Floor[nmax^(1/3)] + 1}]^4, {x, 0, nmax}], x] // Drop[#, 4] &

G.f.: (Sum_{k>=1} x^(k^3))^4.

A340978 Number of ways to write n as an ordered sum of 5 positive cubes.

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 5, 0, 5, 0, 0, 0, 0, 20, 0, 1, 0, 0, 0, 0, 30, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 10, 0, 5, 0, 0, 0, 0, 30, 0, 0, 0, 5, 0, 0, 30, 0, 0, 0, 20, 0, 0, 10, 0, 0, 0, 30, 10, 0, 0, 0, 0, 0, 20, 20, 0, 0, 0, 20, 0, 5, 10

Offset: 5

Ilya Gutkovskiy, Feb 01 2021

nonn

Robert Israel, Table of n, a(n) for n = 5..10000
Index entries for sequences related to sums of cubes

Cf. A000578, A010057, A025458, A051344, A173679, A280618, A340977, A340979, A340980, A340981, A340982, A340983.

b:= proc(n, t) option remember;
      `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add((s->
      `if`(s>n, 0, b(n-s, t-1)))(j^3), j=1..iroot(n, 3))))
    end:
a:= n-> b(n, 5):
seq(a(n), n=5..97);  # Alois P. Heinz, Feb 01 2021

nmax = 97; CoefficientList[Series[Sum[x^(k^3), {k, 1, Floor[nmax^(1/3)] + 1}]^5, {x, 0, nmax}], x] // Drop[#, 5] &

G.f.: (Sum_{k>=1} x^(k^3))^5.

A340979 Number of ways to write n as an ordered sum of 6 positive cubes.

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 6, 0, 15, 0, 0, 0, 0, 30, 0, 6, 0, 0, 0, 0, 60, 0, 1, 0, 0, 0, 0, 60, 0, 0, 0, 0, 15, 0, 30, 0, 0, 0, 0, 60, 0, 6, 0, 6, 0, 0, 90, 0, 0, 0, 30, 0, 0, 60, 0, 0, 0, 60, 20, 0, 15, 0, 0, 0, 60, 60, 0, 0, 0, 30, 0, 30, 60

Offset: 6

Ilya Gutkovskiy, Feb 01 2021

nonn

Robert Israel, Table of n, a(n) for n = 6..10000
Index entries for sequences related to sums of cubes

Cf. A000578, A010057, A025459, A051344, A173680, A280618, A340977, A340978, A340980, A340981, A340982, A340983.

b:= proc(n, t) option remember;
      `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add((s->
      `if`(s>n, 0, b(n-s, t-1)))(j^3), j=1..iroot(n, 3))))
    end:
a:= n-> b(n, 6):
seq(a(n), n=6..98);  # Alois P. Heinz, Feb 01 2021

nmax = 98; CoefficientList[Series[Sum[x^(k^3), {k, 1, Floor[nmax^(1/3)] + 1}]^6, {x, 0, nmax}], x] // Drop[#, 6] &

G.f.: (Sum_{k>=1} x^(k^3))^6.

A340981 Number of ways to write n as an ordered sum of 8 positive cubes.

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, 8, 0, 70, 0, 0, 0, 0, 56, 0, 56, 0, 0, 0, 0, 168, 0, 28, 0, 0, 0, 0, 280, 0, 8, 0, 0, 28, 0, 280, 0, 1, 0, 0, 168, 0, 168, 0, 8, 0, 0, 420, 0, 56, 0, 56, 0, 0, 560, 0, 8, 0, 168, 56, 0, 420, 0, 0, 0, 280, 280, 0, 168

Offset: 8

Ilya Gutkovskiy, Feb 01 2021

Robert Israel, Table of n, a(n) for n = 8..10000
Index entries for sequences related to sums of cubes

Cf. A000578, A010057, A025461, A051344, A173681, A280618, A340977, A340978, A340979, A340980, A340982, A340983.

b:= proc(n, t) option remember;
      `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add((s->
      `if`(s>n, 0, b(n-s, t-1)))(j^3), j=1..iroot(n, 3))))
    end:
a:= n-> b(n, 8):
seq(a(n), n=8..95);  # Alois P. Heinz, Feb 01 2021

nmax = 95; CoefficientList[Series[Sum[x^(k^3), {k, 1, Floor[nmax^(1/3)] + 1}]^8, {x, 0, nmax}], x] // Drop[#, 8] &

G.f.: (Sum_{k>=1} x^(k^3))^8.

A340982 Number of ways to write n as an ordered sum of 9 positive cubes.

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 84, 0, 0, 0, 0, 9, 0, 126, 0, 0, 0, 0, 72, 0, 126, 0, 0, 0, 0, 252, 0, 84, 0, 0, 0, 0, 504, 0, 36, 0, 0, 36, 0, 630, 0, 9, 0, 0, 252, 0, 504, 0, 10, 0, 0, 756, 0, 252, 0, 72, 0, 0, 1260, 0, 72, 0, 252, 84, 0, 1260, 0, 9, 0, 504, 504

Offset: 9

Ilya Gutkovskiy, Feb 01 2021

nonn

Robert Israel, Table of n, a(n) for n = 9..10000
Index entries for sequences related to sums of cubes

Cf. A000578, A010057, A025462, A051344, A173682, A280618, A340977, A340978, A340979, A340980, A340981, A340983.

b:= proc(n, t) option remember;
      `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add((s->
      `if`(s>n, 0, b(n-s, t-1)))(j^3), j=1..iroot(n, 3))))
    end:
a:= n-> b(n, 9):
seq(a(n), n=9..94);  # Alois P. Heinz, Feb 01 2021

nmax = 94; CoefficientList[Series[Sum[x^(k^3), {k, 1, Floor[nmax^(1/3)] + 1}]^9, {x, 0, nmax}], x] // Drop[#, 9] &

G.f.: (Sum_{k>=1} x^(k^3))^9.

A340983 Number of ways to write n as an ordered sum of 10 positive cubes.

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 45, 0, 0, 0, 0, 0, 0, 120, 0, 0, 0, 0, 10, 0, 210, 0, 0, 0, 0, 90, 0, 252, 0, 0, 0, 0, 360, 0, 210, 0, 0, 0, 0, 840, 0, 120, 0, 0, 45, 0, 1260, 0, 45, 0, 0, 360, 0, 1260, 0, 20, 0, 0, 1260, 0, 840, 0, 91, 0, 0, 2520, 0, 360, 0, 360, 120, 0, 3150, 0, 90

Offset: 10

Ilya Gutkovskiy, Feb 01 2021

Robert Israel, Table of n, a(n) for n = 10..10000
Index entries for sequences related to sums of cubes

Cf. A000578, A010057, A025463, A051344, A280618, A340977, A340978, A340979, A340980, A340981, A340982.

b:= proc(n, t) option remember;
      `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add((s->
      `if`(s>n, 0, b(n-s, t-1)))(j^3), j=1..iroot(n, 3))))
    end:
a:= n-> b(n, 10):
seq(a(n), n=10..92);  # Alois P. Heinz, Feb 01 2021

nmax = 92; CoefficientList[Series[Sum[x^(k^3), {k, 1, Floor[nmax^(1/3)] + 1}]^10, {x, 0, nmax}], x] // Drop[#, 10] &

G.f.: (Sum_{k>=1} x^(k^3))^10.

cp's OEIS Frontend

A051344 Number of ways of writing n as a sum of 3 positive cubes (counted naively).

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A340977 Number of ways to write n as an ordered sum of 4 positive cubes.

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A340978 Number of ways to write n as an ordered sum of 5 positive cubes.

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A340979 Number of ways to write n as an ordered sum of 6 positive cubes.

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A340981 Number of ways to write n as an ordered sum of 8 positive cubes.

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A340982 Number of ways to write n as an ordered sum of 9 positive cubes.

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Maple

Mathematica

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A340983 Number of ways to write n as an ordered sum of 10 positive cubes.

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Maple

Mathematica

Formula