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

0,10

Links

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

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}]

Crossrefs

Cf. A000009, A097356.

Sequence in context: A059112 A111731 A369339 * A134992 A073260 A350459

Adjacent sequences: A368865 A368866 A368867 * A368869 A368870 A368871

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 08 2024

Status

approved