cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A341404 Number of nonnegative solutions to (x_1)^2 + (x_2)^2 + ... + (x_9)^2 <= n.

Original entry on oeis.org

1, 10, 46, 130, 265, 463, 799, 1339, 2014, 2780, 3860, 5444, 7301, 9263, 11783, 15263, 19250, 23237, 27893, 34193, 41519, 48701, 56765, 67421, 79484, 91067, 103739, 119855, 138035, 155819, 174923, 198863, 225890, 251444, 277976, 311492, 349122, 384420, 421284
Offset: 0

Views

Author

Ilya Gutkovskiy, Feb 10 2021

Keywords

Comments

Partial sums of A045851.

Links

Crossrefs

Cf. A000122, A000606, A003059, A045851, A055408, A055415, A224212, A224213, A302862, A341400, A341401, A341402, A341403, A341405.

Programs

  • Maple
    b:= proc(n, k) option remember; `if`(n=0, 1, `if`(n<0 or k<1, 0,
      b(n, k-1)+add(b(n-j^2, k-1), j=1..isqrt(n))))
    end:
a:= proc(n) option remember; b(n, 9)+`if`(n>0, a(n-1), 0) end:
seq(a(n), n=0..38);  # Alois P. Heinz, Feb 10 2021
  • Mathematica
    nmax = 38; CoefficientList[Series[(1 + EllipticTheta[3, 0, x])^9/(512 (1 - x)), {x, 0, nmax}], x]

Formula

G.f.: (1 + theta_3(x))^9 / (512 * (1 - x)).
a(n^2) = A055408(n).

A341405 Number of nonnegative solutions to (x_1)^2 + (x_2)^2 + ... + (x_10)^2 <= n.

Original entry on oeis.org

1, 11, 56, 176, 396, 738, 1308, 2268, 3618, 5258, 7449, 10689, 14889, 19609, 25369, 33289, 43154, 53774, 65739, 81339, 100671, 121221, 143421, 171501, 205701, 241283, 278678, 324398, 378998, 435968, 495428, 566468, 650798, 737888, 826083, 930123, 1053323
Offset: 0

Views

Author

Ilya Gutkovskiy, Feb 10 2021

Keywords

Comments

Partial sums of A045852.

Links

Crossrefs

Cf. A000122, A000606, A003059, A045852, A055409, A055416, A224212, A224213, A302862, A341400, A341401, A341402, A341403, A341404.

Programs

  • Maple
    b:= proc(n, k) option remember; `if`(n=0, 1, `if`(n<0 or k<1, 0,
      b(n, k-1)+add(b(n-j^2, k-1), j=1..isqrt(n))))
    end:
a:= proc(n) option remember; b(n, 10)+`if`(n>0, a(n-1), 0) end:
seq(a(n), n=0..36);  # Alois P. Heinz, Feb 10 2021
  • Mathematica
    nmax = 36; CoefficientList[Series[(1 + EllipticTheta[3, 0, x])^10/(1024 (1 - x)), {x, 0, nmax}], x]

Formula

G.f.: (1 + theta_3(x))^10 / (1024 * (1 - x)).
a(n^2) = A055409(n).

A372512 Number of solutions to x^2 + y^2 + z^2 <= n, where x, y, z are positive odd integers.

Original entry on oeis.org

0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 4, 4, 4, 4, 4, 7, 7, 7, 7, 7, 7, 7, 7, 11, 11, 11, 11, 11, 11, 11, 11, 17, 17, 17, 17, 17, 17, 17, 17, 20, 20, 20, 20, 20, 20, 20, 20, 26, 26, 26, 26, 26, 26, 26, 26, 35, 35, 35, 35, 35, 35, 35, 35, 38, 38, 38, 38, 38, 38, 38, 38, 45, 45, 45, 45, 45, 45
Offset: 0

Views

Author

Ilya Gutkovskiy, May 04 2024

Keywords

Links

Crossrefs

Cf. A000606, A008437, A085121, A117609, A211639, A349610, A372511.

Programs

  • Mathematica
    nmax = 80; CoefficientList[Series[EllipticTheta[2, 0, x^4]^3/(8 (1 - x)), {x, 0, nmax}], x]
Previous Showing 11-13 of 13 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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