A109037 Number of irreducible partitions into triangular numbers. A partition is irreducible if no subpartition with 2 or more parts sums to a triangular number.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 2, 2, 3, 3, 3, 1, 2, 3, 3, 3, 4, 2, 1, 2, 5, 4, 5, 5, 3, 4, 1, 3, 2, 3, 6, 5, 4, 5, 5, 1, 4, 6, 5, 4, 8, 5, 6, 9, 10, 1, 3, 5, 9, 9, 10, 9, 9, 10, 7, 6, 1, 4, 10, 9, 7, 11, 7, 8, 12, 14, 7, 11, 1, 9, 13, 9, 12, 9, 9, 15, 16, 12, 11, 16, 15, 1, 8, 11, 8, 16

Offset

0,13

Comments

Sequence is almosot certainly unbounded. Obviously it contains infinitely many 1's, at triangular indices. At non-triangular indices, series appears to go to infinity, but this is conjecture and growth rate is entirely unknown. Also unknown is whether the sequence is onto the positive integers.

Links

Table of n, a(n) for n=0..95.

Example

a(9)=1 for the partition [6,3]. [6,1^3], [3^3], [3^2,1^3], [3,1^6] and [1^9] are all excluded because they contain subpartitions [3^2] or [1^3] summing to a triangular number.

Crossrefs

Cf: A007294, A109038, A109035.

Sequence in context: A241900 A204018 A261915 * A366136 A366693 A147680

Adjacent sequences: A109034 A109035 A109036 * A109038 A109039 A109040

Keyword

nonn

Author

Franklin T. Adams-Watters, Jun 16 2005

Status

approved