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A341397
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Number of integer solutions to (x_1)^2 + (x_2)^2 + ... + (x_8)^2 <= n.
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4
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1, 17, 129, 577, 1713, 3729, 6865, 12369, 21697, 33809, 47921, 69233, 101041, 136209, 174737, 231185, 306049, 384673, 469457, 579217, 722353, 876465, 1025649, 1220337, 1481521, 1733537, 1979713, 2306753, 2697537, 3087777, 3482913, 3959585, 4558737, 5155473
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OFFSET
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0,2
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COMMENTS
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Partial sums of A000143.
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LINKS
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Table of n, a(n) for n=0..33.
Index entries for sequences related to sums of squares
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FORMULA
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G.f.: theta_3(x)^8 / (1 - x).
a(n^2) = A055414(n).
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MAPLE
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b:= proc(n, k) option remember; `if`(n=0, 1, `if`(n<0 or k<1, 0,
b(n, k-1)+2*add(b(n-j^2, k-1), j=1..isqrt(n))))
end:
a:= proc(n) option remember; b(n, 8)+`if`(n>0, a(n-1), 0) end:
seq(a(n), n=0..33); # Alois P. Heinz, Feb 10 2021
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MATHEMATICA
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nmax = 33; CoefficientList[Series[EllipticTheta[3, 0, x]^8/(1 - x), {x, 0, nmax}], x]
Table[SquaresR[8, n], {n, 0, 33}] // Accumulate
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CROSSREFS
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Cf. A000122, A000143, A001650, A046895, A055407, A055414, A057655, A117609, A122510, A175360, A175361, A302860, A341396, A341398, A341399.
Sequence in context: A114756 A336186 A159563 * A229516 A352114 A279637
Adjacent sequences: A341394 A341395 A341396 * A341398 A341399 A341400
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KEYWORD
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nonn
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AUTHOR
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Ilya Gutkovskiy, Feb 10 2021
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STATUS
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approved
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