A213457 Intertwining numbers. (Formerly M1988)

1, 1, 2, 10, 148, 7384, 1380960, 1058349286

Offset

1,3

Comments

a(4)=10 for example is the number of ways of arranging 1 a, 2 b's, 3 c's and 4 d's so that if we look at any two letters, i and j say, with i<j, then any pair of i's are separated and surrounded by at least one j.

If the condition is imposed only on pairs of consecutive letters, we get A003121.

References

C. L. Mallows, Letter to N. J. A. Sloane, Nov 11 1980

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=1..8.

Georg Fischer, Perl program

Example

The 10 sequences for n=4 are dcbadcbdcd dcbadcdbcd dcbdacbdcd dcbdacdbcd dcbdcabdcd dcbdcadbcd dcbdcdabcd dcdbacdbcd dcdbcadbcd dcdbcdabcd.
For example in dcbdacdbcd we see
..ba...b..
.cb..c.bc.
d.bd..db.d
dc.d.cd.cd

Crossrefs

Cf. A003121.

Sequence in context: A188490 A317075 A295207 * A060595 A303440 A086619

Adjacent sequences: A213454 A213455 A213456 * A213458 A213459 A213460

Keyword

nonn,more

Author

N. J. A. Sloane. Entry revised and given a new A-number by N. J. A. Sloane, Jun 13 2012. The old entry was A004065.

Extensions

a(7) from David W. Wilson, Dec 11 1999

Definition clarified by David Applegate, Jun 14 2012

a(8) from Georg Fischer, Mar 21 2018

Status

approved