A368868 Number of partitions of n into odd parts not greater than sqrt(n).

1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 29, 31, 33, 35, 37, 40, 42, 44, 47, 49, 52, 55, 57, 60, 63, 66, 69, 72, 75, 78, 82, 85, 88, 92, 292, 308, 324, 341, 358, 376, 395, 414, 434, 454, 475, 497, 519, 542, 566, 590, 615, 641, 667, 694, 722, 751

Offset: 0

Author

Ilya Gutkovskiy, Jan 08 2024

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000009, A097356.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      b(n, i-1)+`if`(i::odd, b(n-i, min(n-i, i)), 0)))
    end:
a:= n-> b(n, floor(sqrt(n))):
seq(a(n), n=0..70);  # Alois P. Heinz, Jan 13 2024

Mathematica

Table[SeriesCoefficient[Product[1/(1 - Boole[OddQ[k]] x^k), {k, 1, Floor[Sqrt[n]]}], {x, 0, n}], {n, 0, 70}]