A298934 Number of partitions of n^2 into distinct cubes.
1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 3, 1, 0, 0, 0, 0, 0, 0, 3, 3, 1, 0, 3, 0, 2, 4, 0, 0, 1, 0, 0, 2, 3, 1, 1, 0, 6, 3, 6, 1, 6, 0, 3, 9, 0, 6, 6, 7, 0, 10, 3, 3, 6, 0, 8, 6, 13, 2, 10, 9, 10, 19, 2, 14, 21, 7, 2, 25
Offset: 0
Keywords
Examples
a(15) = 2 because we have [216, 8, 1] and [125, 64, 27, 8, 1].
Links
Crossrefs
Programs
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Maple
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(n>i^2*(i+1)^2/4, 0, b(n, i-1)+ `if`(i^3>n, 0, b(n-i^3, i-1)))) end: a:= n-> b(n^2, n): seq(a(n), n=0..100); # Alois P. Heinz, Jan 29 2018 -
Mathematica
Table[SeriesCoefficient[Product[1 + x^k^3, {k, 1, Floor[n^(2/3) + 1]}], {x, 0, n^2}], {n, 0, 84}]