

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
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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}] (* JeanFrançois 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



