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A063730 Number of solutions to w^2 + x^2 + y^2 + z^2 = n in positive integers. 4
0, 0, 0, 0, 1, 0, 0, 4, 0, 0, 6, 0, 4, 4, 0, 12, 1, 0, 12, 4, 6, 4, 12, 12, 0, 12, 6, 12, 12, 0, 24, 16, 0, 12, 18, 12, 13, 16, 12, 28, 6, 0, 36, 16, 12, 24, 24, 24, 4, 16, 30, 24, 18, 12, 36, 36, 0, 28, 42, 12, 36, 16, 24, 52, 1, 24, 48, 28, 18, 24, 60, 36, 12 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,8

LINKS

T. D. Noe, Table of n, a(n) for n = 0..10000

Index entries for sequences related to sums of squares

FORMULA

G.f.: (Sum_{m>=1} x^(m^2))^4.

a(n) = ( A000118(n) - 4*A005875(n) + 6*A004018(n) - 4*A000122(n) + A000007(n) )/16. - Max Alekseyev, Sep 29 2012

G.f.: ((theta_3(q) - 1)/2)^4, where theta_3() is the Jacobi theta function. - Ilya Gutkovskiy, Aug 08 2018

MATHEMATICA

r[n_] := Reduce[ w > 0 && x > 0 && y > 0 && z > 0 && w^2 + x^2 + y^2 + z^2 == n, {w, x, y, z}, Integers]; a[n_] := Which[rn = r[n]; rn === False, 0, Head[rn] === Or, Length[rn], True, 1]; Table[a[n], {n, 0, 72}] (* Jean-François Alcover, Jul 22 2013 *)

PROG

(PARI) seq(n)=Vec((sum(k=1, sqrtint(n), x^(k^2)) + O(x*x^n))^4 + O(x*x^n), -(n+1)) \\ Andrew Howroyd, Aug 08 2018

CROSSREFS

Cf. A063691, A063725.

Sequence in context: A193108 A212044 A290335 * A131431 A240664 A255328

Adjacent sequences:  A063727 A063728 A063729 * A063731 A063732 A063733

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Aug 23 2001

STATUS

approved

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Last modified November 13 19:25 EST 2018. Contains 317149 sequences. (Running on oeis4.)