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A213024 The number of solutions to x^2 + y^2 + 2*z^2 = n in positive integers x,y,z. 3
0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, 1, 0, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 6, 0, 0, 4, 0, 2, 4, 2, 3, 4, 2, 2, 2, 0, 6, 4, 2, 4, 0, 4, 2, 4, 2, 0, 8, 2, 2, 6, 0, 2, 8, 2, 6, 4, 0, 6, 1, 0, 4, 6, 4, 4, 6, 2, 2, 6, 2, 4, 8, 4, 0, 4, 2, 2, 10, 4, 6, 4, 2, 6, 2, 2, 8, 6, 6, 6, 0, 2, 0, 8, 6, 2, 9 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,8

REFERENCES

Mohammad K. Azarian, Diophantine Pair, Problem B-881, Fibonacci Quarterly, Vol. 37, No. 3, August 1999, pp. 277-278.  Solution published in Vol. 38, No. 2, May 2000, pp. 183-184.

LINKS

Table of n, a(n) for n=0..100.

FORMULA

a(n) = ( A014455(n) - 2*A033715(n) - A004018(n) + A000122(n/2) + 2*A000122(n) - A000007(n) )/8.

G.f.: T(x)^2 * T(x^2) where T(x) = sum(k>=1, x^(k^2)). [Joerg Arndt, Oct 01 2012]

PROG

(PARI)

N=166; x='x+O('x^N);

T(x)=sum(k=1, 1+sqrtint(N), x^(k*k) );

gf=T(x)^2 * T(x^2);

v=Vec('a0 + gf );  v[1]=0;  v

/* Joerg Arndt, Oct 01 2012 */

CROSSREFS

Cf. A156384

Sequence in context: A308046 A289323 A086937 * A291289 A095759 A260309

Adjacent sequences:  A213021 A213022 A213023 * A213025 A213026 A213027

KEYWORD

nonn

AUTHOR

Max Alekseyev, Sep 29 2012

STATUS

approved

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Last modified October 22 09:56 EDT 2019. Contains 328315 sequences. (Running on oeis4.)