A181786 - OEIS

A181786

Number of inequivalent solutions to n^2 = a^2 + b^2 + c^2 with positive a, b, c.

0, 0, 0, 1, 0, 0, 1, 1, 0, 3, 0, 2, 1, 1, 1, 3, 0, 2, 3, 3, 0, 6, 2, 3, 1, 2, 1, 8, 1, 3, 3, 4, 0, 10, 2, 5, 3, 4, 3, 8, 0, 5, 6, 6, 2, 11, 3, 6, 1, 8, 2, 12, 1, 6, 8, 8, 1, 15, 3, 8, 3, 7, 4, 20, 0, 6, 10, 9, 2, 16, 5, 9, 3, 9, 4, 15, 3, 15, 8, 10, 0, 22, 5, 11, 6, 9, 6, 18, 2, 11, 11, 14, 3, 21, 6, 13, 1, 12, 8, 31, 2

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OFFSET

0,10

COMMENTS

Note that a(n)=0 for n=0 and the n in A094958.

Also note that a(2n)=a(n), e.g., a(1000)=a(500)=a(250)=a(125)=14. - Zak Seidov, Mar 02 2012

a(n) is the number of distinct parallelepipeds each one having integer diagonal n and integer sides. - César Eliud Lozada, Oct 26 2014

LINKS

Samuel Harkness, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Zak Seidov)

MATHEMATICA

nn=100; t=Table[0, {nn}]; Do[n=Sqrt[a^2+b^2+c^2]; If[n<=nn && IntegerQ[n], t[[n]]++], {a, nn}, {b, a, nn}, {c, b, nn}]; Prepend[t, 0]

CROSSREFS

Cf. A016725, A016727, A046080, A181787, A181788

Sequence in context: A275326 A092926 A052311 * A164629 A100950 A359867

Adjacent sequences: A181783 A181784 A181785 * A181787 A181788 A181789

KEYWORD

nonn

AUTHOR

T. D. Noe, Nov 12 2010

STATUS

approved