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A357354
Number of partitions of n into distinct positive squares such that the number of parts is a square.
2
1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 3, 1, 0, 2, 0, 0, 1, 1, 1
OFFSET
0,79
LINKS
EXAMPLE
a(30) = 1 because we have [16,9,4,1].
a(78) = 3: [36,25,16,1], [49,16,9,4], [64,9,4,1].
MAPLE
b:= proc(n, i, t) option remember; `if`(n=0,
`if`(issqr(t), 1, 0), `if`(n>i*(i+1)*(2*i+1)/6, 0,
`if`(i^2>n, 0, b(n-i^2, i-1, t+1))+b(n, i-1, t)))
end:
a:= n-> b(n, isqrt(n), 0):
seq(a(n), n=0..100); # Alois P. Heinz, Sep 25 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Sep 25 2022
STATUS
approved