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A340977
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Number of ways to write n as an ordered sum of 4 positive cubes.
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9
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1, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 1, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 4, 0, 0, 6, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 12, 4, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 24
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OFFSET
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4,8
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LINKS
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FORMULA
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G.f.: (Sum_{k>=1} x^(k^3))^4.
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MAPLE
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b:= proc(n, t) option remember;
`if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add((s->
`if`(s>n, 0, b(n-s, t-1)))(j^3), j=1..iroot(n, 3))))
end:
a:= n-> b(n, 4):
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MATHEMATICA
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nmax = 100; CoefficientList[Series[Sum[x^(k^3), {k, 1, Floor[nmax^(1/3)] + 1}]^4, {x, 0, nmax}], x] // Drop[#, 4] &
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CROSSREFS
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Cf. A000578, A010057, A025457, A051344, A173678, A280618, A340978, A340979, A340980, A340981, A340982, A340983.
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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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