A375099 Number of partitions of [n] into blocks whose element sum is <= n.

1, 1, 1, 2, 3, 6, 12, 26, 57, 141, 333, 885, 2259, 6391, 17302, 51685, 147937, 460561, 1389093, 4504136, 14127767, 47719998, 155559696, 542178148, 1835105103, 6600158865, 23035501468, 85428655084, 307266398440, 1168951871972, 4331125790382, 16897269822235

Offset

0,4

Links

Table of n, a(n) for n=0..31.

Wikipedia, Partition of a set

Example

a(0) = 1: the empty partition.
a(1) = 1: 1.
a(2) = 1: 1|2.
a(3) = 2: 12|3, 1|2|3.
a(4) = 3: 12|3|4, 13|2|4, 1|2|3|4.
a(5) = 6: 12|3|4|5, 13|2|4|5, 14|23|5, 1|23|4|5, 14|2|3|5, 1|2|3|4|5.
a(6) = 12: 123|4|5|6, 12|3|4|5|6, 13|24|5|6, 13|2|4|5|6, 14|23|5|6, 15|23|4|6, 1|23|4|5|6, 14|2|3|5|6, 15|24|3|6, 1|24|3|5|6, 15|2|3|4|6, 1|2|3|4|5|6.

Crossrefs

Main diagonal of A374932.

Row sums of A375023.

Cf. A000110, A369079.

Sequence in context: A367386 A166296 A151527 * A086625 A152172 A001677

Adjacent sequences: A375096 A375097 A375098 * A375100 A375101 A375102

Keyword

nonn

Author

Alois P. Heinz, Jul 29 2024

Status

approved