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A025458
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Number of partitions of n into 5 positive cubes.
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3
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0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0
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OFFSET
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0,158
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COMMENTS
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a(n) > 2 at n= 766, 810, 827, 829, 865, 883, 981, 1018, 1025, 1044,... - R. J. Mathar, Sep 15 2015
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LINKS
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FORMULA
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a(n) = [x^n y^5] Product_{k>=1} 1/(1 - y*x^(k^3)). - Ilya Gutkovskiy, Apr 23 2019
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MAPLE
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local a, x, y, z, u, vcu ;
a := 0 ;
for x from 1 do
if 5*x^3 > n then
return a;
end if;
for y from x do
if x^3+4*y^3 > n then
break;
end if;
for z from y do
if x^3+y^3+3*z^3 > n then
break;
end if;
for u from z do
if x^3+y^3+z^3+2*u^3 > n then
break;
end if;
vcu := n-x^3-y^3-z^3-u^3 ;
if isA000578(vcu) then
a := a+1 ;
end if;
end do:
end do:
end do:
end do:
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MATHEMATICA
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a[n_] := IntegerPartitions[n, {5}, Range[n^(1/3) // Ceiling]^3] // Length;
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CROSSREFS
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Column 5 of A320841, which cross-references the equivalent sequences for other numbers of positive cubes.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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