A272301 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 or i member of c and i+1 member of b.

1, 1, 2, 4, 9, 23, 66, 204, 664, 2273, 8283, 32463, 136434, 605848

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) = 9: 1234, 123|4, 124|3, 12|34, 134|2, 13|24, 14|23, 1|234, 14|2|3.
a(5) = 23: 12345, 1234|5, 1235|4, 123|45, 1245|3, 124|35, 125|34, 12|345, 125|3|4, 1345|2, 134|25, 135|24, 13|245, 13|25|4, 145|23, 14|235, 15|234, 1|2345, 15|23|4, 145|2|3, 14|25|3, 14|2|35, 15|2|34.
a(6) = 66: 123456, 12345|6, 12346|5, 1234|56, 12356|4, 1235|46, 1236|45, 123|456, 1236|4|5, 12456|3, 1245|36, 1246|35, 124|356, 124|36|5, 1256|34, 125|346, 126|345, 12|3456, 126|34|5, 1256|3|4, 125|36|4, 125|3|46, 126|3|45, 13456|2, 1345|26, 1346|25, 134|256, 134|26|5, 1356|24, 135|246, 136|245, 13|2456, 136|24|5, 136|25|4, 13|256|4, 13|25|46, 13|26|45, 1456|23, 145|236, 146|235, 14|2356, 14|236|5, 156|234, 15|2346, 16|2345, 1|23456, 16|234|5, 156|23|4, 15|236|4, 15|23|46, 16|23|45, 1456|2|3, 145|26|3, 145|2|36, 146|25|3, 14|256|3, 14|25|36, 146|2|35, 14|26|35, 14|2|356, 15|24|36, 16|24|35, 156|2|34, 15|26|34, 15|2|346, 16|2|345.

Crossrefs

Cf. A000110, A185982, A271270, A272064, A272105.

Sequence in context: A245162 A007476 A202552 * A359032 A129698 A261134

Adjacent sequences: A272298 A272299 A272300 * A272302 A272303 A272304

Keyword

nonn,more

Author

Alois P. Heinz, Apr 25 2016

Status

approved