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A357352
Number of partitions of n into distinct positive triangular numbers such that the number of parts is a triangular number.
2
1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 1, 0, 1, 0, 2, 0, 1, 1, 0, 1, 1, 1, 0, 3, 0, 1, 1, 2, 0, 1, 1, 1, 3, 0, 2, 1, 1, 1, 1, 2, 2, 2, 1, 0, 3, 1, 0, 4, 1, 2, 2, 2, 1, 2, 2, 1, 3, 1, 3, 2, 1, 3, 3, 1, 2, 3, 3, 2, 2, 3, 1, 3, 3, 2, 4, 2, 2, 6, 2, 4, 2, 4
OFFSET
0,11
LINKS
EXAMPLE
a(56) = 2 because we have [45,10,1] and [21,15,10,6,3,1].
MAPLE
b:= proc(n, i, t) option remember; (h-> `if`(n=0,
`if`(issqr(8*t+1), 1, 0), `if`(n>i*(i+1)*(i+2)/6, 0,
`if`(h>n, 0, b(n-h, i-1, t+1))+b(n, i-1, t))))(i*(i+1)/2)
end:
a:= n-> b(n, floor((sqrt(1+8*n)-1)/2), 0):
seq(a(n), n=0..100); # Alois P. Heinz, Sep 25 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Sep 25 2022
STATUS
approved