



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
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OFFSET

1,2


COMMENTS

Let b(n) = nth 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 "particleinabox" model in elementary quantum mechanics.  A. Timothy Royappa, Jan 09 2009


REFERENCES

G. M. Barrow, Physical Chemistry (6th ed.), McGrawHill, 1996, p. 69.


LINKS

Daniel Leary, Table of n, a(n) for n = 1..8283


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: A163644 A339901 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



