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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.
1
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
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
Sequence in context: A183027 A359227 A078178 * A355035 A105068 A363274
KEYWORD
nonn
AUTHOR
A. Timothy Royappa, Feb 12 2019
EXTENSIONS
Offset changed to 1 by Jinyuan Wang, Feb 20 2020
STATUS
approved