A064480 Form a conjugate partition of row with 1+1+1 in first row. all other rows are the union of their parents. a(n) = number of types of piles in the n-th row.

1, 2, 3, 5, 7, 10, 13, 19, 26, 36, 51, 69, 94, 130, 188, 261, 366, 514, 710, 993, 1399, 1995, 2779, 3912, 5490, 7723, 10848, 15230, 21457, 30165, 42401, 59718, 83808, 117844, 165932, 233358, 328316, 461885, 650105, 915243, 1287795, 1812815, 2552260, 3593697

Offset

1,2

Comments

The n-th row sum is equal to 3*2^(n-1).

The largest part of the n-th row is A000204(n).

Links

Table of n, a(n) for n=1..44.

Sean A. Irvine, Java program (github)

Example

Start with 1+1+1 from which a(1)=1.
The conjugate of 1+1+1 is 3, giving the union 3+1+1+1, and a(2)=2.
The conjugate of 3+1+1+1 is 4+1+1, giving the union 4+3+1+1+1+1+1, and a(3)=3.
The conjugate of 4+3+1+1+1+1+1 is 7+2+2+1, giving the union 7+4+3+2+2+1+1+1+1+1+1, and a(4)=5.

Crossrefs

Cf. A000700, A000701, A000204.

Sequence in context: A005691 A035954 A023192 * A274111 A209000 A115024

Adjacent sequences: A064477 A064478 A064479 * A064481 A064482 A064483

Keyword

nonn

Author

Naohiro Nomoto, Feb 14 2002

Extensions

More terms from Sean A. Irvine, Jul 13 2023

Status

approved