A064660 The number of distinct parts in the partition sequence lambda(n) formed by the recurrence lambda(1) = 1 and lambda(n+1) is the sum of lambda(n) and its conjugate.

1, 1, 2, 3, 4, 6, 8, 11, 15, 22, 30, 39, 53, 75, 106, 151, 215, 297, 424, 592, 835, 1162, 1618, 2274, 3217, 4556, 6361, 8940, 12560, 17645, 24822, 34812, 48967, 68861, 96939, 136462, 191896, 269976, 379726, 534239, 751829, 1058170, 1489038, 2096243, 2951262

Offset

1,3

Comments

lambda(n) is a partition of 2^(n-1).

The largest part of lambda(n) is A000045(n).

The number of parts of lambda(n) is A000045(n+1). Peter J. Taylor, Jul 24 2014

Links

Table of n, a(n) for n=1..45.

Example

lambda(4) = 3+2+1+1+1 has conjugate partition 5+2+1, so lambda(5) = 5+3+2+2+1+1+1+1 and a(5) = |{5,3,2,1}| = 4.

Crossrefs

Cf. A000700, A000701, A000045.

Sequence in context: A003411 A034081 A289432 * A321359 A321567 A066806

Adjacent sequences: A064657 A064658 A064659 * A064661 A064662 A064663

Keyword

nonn

Author

Naohiro Nomoto, Feb 14 2002

Extensions

More terms, description and example rephrased by Peter J. Taylor, Jul 24 2014

Status

approved