A339246 a(n) = 1 for n <= 2; thereafter a(n) is the number of partitions of n where every part k appears at least a(k) times.

1, 1, 1, 2, 3, 3, 5, 5, 7, 8, 10, 11, 15, 16, 20, 23, 28, 31, 38, 41, 50, 56, 66, 72, 86, 94, 110, 122, 140, 154, 178, 195, 223, 245, 276, 303, 344, 376, 421, 461, 513, 561, 627, 681, 756, 824, 909, 988, 1092, 1182, 1301, 1413, 1547, 1673, 1834, 1979, 2165, 2341, 2548, 2746, 2993

Offset

0,4

Links

Table of n, a(n) for n=0..60.

Index entries for sequences related to partitions

Formula

G.f.: -x^2 + Product_{k>=1} (1 + x^(a(k)*k) / (1 - x^k)).

Example

a(0) = a(1) = a(2) = 1: by definition.
a(3) = 2: [2, 1], [1, 1, 1].
a(4) = 3: [2, 2], [2, 1, 1], [1, 1, 1, 1].
a(5) = 3: [2, 2, 1], [2, 1, 1, 1], [1, 1, 1, 1, 1].
a(6) = 5: [3, 3], [2, 2, 2], [2, 2, 1, 1], [2, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1].

Crossrefs

Cf. A115584, A117144, A151945.

Sequence in context: A210336 A280271 A145834 * A341142 A130006 A099609

Adjacent sequences: A339243 A339244 A339245 * A339247 A339248 A339249

Keyword

nonn

Author

Ilya Gutkovskiy, Nov 28 2020

Status

approved