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

Author

Naohiro Nomoto, Feb 14 2002

Keywords

• nonn

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

Examples

			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.

Extensions

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