A306396 Consider the numbers in A024796, numbers expressible in more than one way as i^2 + j^2 + k^2, where 1 <= i <= j <= k; sequence number of ways these numbers can be expressed.

2, 2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 3, 3, 2, 2, 2, 3, 3, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 2, 2, 2, 3, 4, 3, 2, 4, 2, 2, 2, 2, 4, 2, 3, 3, 2, 4, 2, 2, 2, 4, 3, 2, 2, 3, 2, 4, 3, 3, 2, 2, 3, 2, 3, 3, 3, 2, 4, 5, 2, 2, 4, 4, 2, 2, 5, 6, 2, 2, 2, 2, 3, 2, 2, 3, 3, 3, 3, 2, 3, 2, 2, 5, 3, 4, 2, 3, 2, 3, 3, 4, 3, 4, 2, 4, 2, 4, 4, 4, 3, 2, 4, 2, 3, 5, 2, 5, 4, 2

Offset

1,1

Comments

Number of accidental degeneracies in the quantum mechanical 3-D "particle-in-a-box" model.

Links

Jinyuan Wang, Table of n, a(n) for n = 1..1000

Formula

a(n) = A025427(A024796(n)).

Example

The fourth term in A024796 is 41, which can be expressed in two ways as the sum of three nonzero squares (1^2 + 2^2 + 6^2 or 3^2 + 4^2 + 4^2), so a(4) = 2.

Mathematica

r[n_] := Length@ IntegerPartitions[n, {3}, Range[Sqrt[n]]^2]; Select[ Array[r, 300], # > 1 &] (* Giovanni Resta, Feb 21 2020 *)

Crossrefs

Cf. A024796, A025427.

Sequence in context: A183027 A359227 A078178 * A355035 A105068 A363274

Adjacent sequences: A306393 A306394 A306395 * A306397 A306398 A306399

Keyword

nonn

Author

A. Timothy Royappa, Feb 12 2019

Extensions

Offset changed to 1 by Jinyuan Wang, Feb 20 2020

Status

approved