A387612 a(n) = denominator(Integral_{(x,y,z) in R^3 : 0 <= x^2 + y^2 + z^2 <= n^2}(x^2 + y^2) dx dy dz).

1, 15, 15, 5, 15, 3, 5, 15, 15, 5, 3, 15, 5, 15, 15, 1, 15, 15, 5, 15, 3, 5, 15, 15, 5, 3, 15, 5, 15, 15, 1, 15, 15, 5, 15, 3, 5, 15, 15, 5, 3, 15, 5, 15, 15, 1, 15, 15, 5, 15, 3, 5, 15, 15, 5, 3, 15, 5, 15, 15, 1, 15, 15, 5, 15, 3, 5, 15, 15, 5, 3, 15, 5, 15, 15, 1, 15, 15, 5, 15

Offset

0,2

Comments

The integral gives the moment of inertia of a sphere of radius n.

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1000

Mathematics Stack Exchange, Moment of inertia of a sphere, 2017.

R. Nave, Moment of inertia: Sphere, HyperPhysics.

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

Formula

a(n) = denominator(8*n^5/15).

a(n) = 15/gcd(15,n). - Chai Wah Wu, Sep 08 2025

G.f.: (1 + 15*x + 15*x^2 + 5*x^3 + 15*x^4 + 3*x^5 + 5*x^6 + 15*x^7 + 15*x^8 + 5*x^9 + 3*x^10 + 15*x^11 + 5*x^12 + 15*x^13 + 15*x^14)/(1 - x^15). - Andrew Howroyd, Nov 06 2025

Mathematica

a[n_]:=Denominator[8n^5/15]; Array[a, 80, 0]

Prog

(Python)
def A387612(n): return ((bool(n%3)<<1)+1)*((bool(n%5)<<2)+1) # Chai Wah Wu, Sep 08 2025

Crossrefs

Cf. A000584, A387611 (numerators).

Sequence in context: A280313 A291369 A069785 * A290850 A290669 A173430

Adjacent sequences: A387609 A387610 A387611 * A387613 A387614 A387615

Keyword

nonn,easy,frac

Author

Stefano Spezia, Sep 03 2025

Status

approved