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A014465 A063691 without zeros. 0
1, 3, 3, 3, 1, 6, 3, 3, 3, 6, 3, 3, 6, 4, 6, 6, 6, 3, 6, 3, 9, 9, 6, 3, 3, 6, 6, 1, 6, 6, 6, 6, 12, 6, 6, 9, 6, 12, 6, 12, 3, 3, 12, 6, 3, 3, 12, 7, 3, 12, 6, 12, 3, 9, 6, 15, 3, 15, 12, 6, 6, 12, 3, 3, 12, 9, 18, 6, 6, 12, 6, 9, 4, 6, 18, 9, 12, 6, 6, 12, 9, 6, 9, 12, 6, 12, 18, 18, 15, 6, 6, 21, 3, 9, 12, 9, 6, 12 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Let b(n) = n-th number of form x^2+y^2+z^2, x,y,z >= 1 (A000408); a(n) = number of solutions (x,y,z) to x^2+y^2+z^2=b(n).

The a(n) are also the degeneracies of the energy levels E(n) in the three dimensional cubic "particle-in-a-box" model in elementary quantum mechanics. - A. Timothy Royappa, Jan 09 2009

REFERENCES

G. M. Barrow, Physical Chemistry (6th ed.), McGraw-Hill, 1996, p. 69.

LINKS

Table of n, a(n) for n=1..98.

EXAMPLE

b(1) = 3 = 1^2+1^2+1^2 (1 way), so a(1) = 1; b(2) = 6 = 2^2+1^2+1^2 (3 ways), so a(2) = 3; etc.

PROG

(PARI) for(n=1, 200, r=sqrtint(n); s=0; for(i=1, r, si=i*i; for(j=1, r, sj=j*j; for(k=1, r, if(si+sj+k*k==n, s=s+1)))); if(s, print1(s, ", "))) /* Ralf Stephan, Aug 31 2013 */

CROSSREFS

Sequence in context: A201277 A163644 A290348 * A226645 A243095 A304586

Adjacent sequences:  A014462 A014463 A014464 * A014466 A014467 A014468

KEYWORD

nonn,easy

AUTHOR

A. Timothy Royappa, 1997; entry revised Jun 13 2003

EXTENSIONS

More terms and better name from Ralf Stephan, Aug 31 2013

STATUS

approved

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Last modified April 7 10:45 EDT 2020. Contains 333301 sequences. (Running on oeis4.)