A272105 Number of set partitions of [n] such that for each pair of blocks (b,c) with b<c at least one pair of consecutive numbers (i,i+1) exists with i member of b and i+1 member of c.

1, 1, 2, 4, 8, 17, 41, 115, 362, 1208, 4112, 14107, 49187, 178049

Offset

0,3

Links

Table of n, a(n) for n=0..13.

Wikipedia, Partition of a set

Example

a(3) = 4: 123, 12|3, 13|2, 1|23.
a(4) = 8: 1234, 123|4, 124|3, 12|34, 134|2, 13|24, 14|23, 1|234.
a(5) = 17: 12345, 1234|5, 1235|4, 123|45, 1245|3, 124|35, 125|34, 12|345, 1345|2, 134|25, 135|24, 13|245, 145|23, 14|235, 15|234, 1|2345, 14|2|35.
a(6) = 41: 123456, 12345|6, 12346|5, 1234|56, 12356|4, 1235|46, 1236|45, 123|456, 12456|3, 1245|36, 1246|35, 124|356, 1256|34, 125|346, 126|345, 12|3456, 125|3|46, 13456|2, 1345|26, 1346|25, 134|256, 1356|24, 135|246, 136|245, 13|2456, 13|25|46, 1456|23, 145|236, 146|235, 14|2356, 156|234, 15|2346, 16|2345, 1|23456, 15|23|46, 145|2|36, 146|2|35, 14|26|35, 14|2|356, 15|24|36, 15|2|346.

Crossrefs

Cf. A000110, A185982, A271270, A272064, A272301.

Sequence in context: A331686 A156805 A200542 * A367114 A283162 A364210

Adjacent sequences: A272102 A272103 A272104 * A272106 A272107 A272108

Keyword

nonn,more

Author

Alois P. Heinz, Apr 20 2016

Status

approved