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A341425 Number of positive solutions to (x_1)^2 + (x_2)^2 + ... + (x_6)^2 <= n^2. 7
7, 48, 331, 1269, 3698, 9382, 20927, 42683, 79844, 142173, 238810, 387615, 603589, 915324, 1345294, 1939221, 2729723, 3783313, 5138567, 6895632, 9108626, 11909496, 15362753, 19642539, 24832744, 31179476, 38757032, 47877886, 58647957, 71447776, 86391220 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

LINKS

Alois P. Heinz, Table of n, a(n) for n = 3..1000

Index entries for sequences related to sums of squares

FORMULA

a(n) is the coefficient of x^(n^2) in expansion of (theta_3(x) - 1)^6 / (64 * (1 - x)).

MAPLE

b:= proc(n, k) option remember; `if`(k=0, 1, `if`(n=0, 0,

      add((s->`if`(s>n, 0, b(n-s, k-1)))(j^2), j=1..isqrt(n))))

    end:

a:= n-> b(n^2, 6):

seq(a(n), n=3..33);  # Alois P. Heinz, Feb 11 2021

MATHEMATICA

Table[SeriesCoefficient[(EllipticTheta[3, 0, x] - 1)^6/(64 (1 - x)), {x, 0, n^2}], {n, 3, 33}]

CROSSREFS

Cf. A000122, A001182, A055405, A055412, A175361, A253663, A302995, A340905, A341401, A341423, A341424, A341426, A341427, A341428, A341429.

Sequence in context: A242630 A004187 A180167 * A186653 A231378 A024092

Adjacent sequences:  A341422 A341423 A341424 * A341426 A341427 A341428

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Feb 11 2021

STATUS

approved

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Last modified June 16 21:55 EDT 2021. Contains 345080 sequences. (Running on oeis4.)