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A341396
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Number of integer solutions to (x_1)^2 + (x_2)^2 + ... + (x_7)^2 <= n.
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6
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1, 15, 99, 379, 953, 1793, 3081, 5449, 8893, 12435, 16859, 24419, 33659, 42115, 53203, 69779, 88273, 106081, 125821, 153541, 187981, 217437, 248741, 298469, 351277, 394691, 446939, 515259, 589307, 657683, 728803, 828259, 939223, 1029159, 1124023, 1260103
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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G.f.: theta_3(x)^7 / (1 - x).
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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, 7)+`if`(n>0, a(n-1), 0) end:
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MATHEMATICA
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nmax = 35; CoefficientList[Series[EllipticTheta[3, 0, x]^7/(1 - x), {x, 0, nmax}], x]
Table[SquaresR[7, n], {n, 0, 35}] // Accumulate
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PROG
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(PARI) my(q='q+O('q^(55))); Vec((eta(q^2)^5/(eta(q)^2*eta(q^4)^2))^7/(1-q)) \\ Joerg Arndt, Jun 21 2024
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CROSSREFS
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Cf. A000122, A001650, A008451, A046895, A055406, A055413, A057655, A117609, A122510, A175360, A175361, A302860, A341397, A341398, A341399.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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