A109038 Number of irreducible partitions into smaller triangular numbers. A partition is irreducible if no subpartition with 2 or more parts sums to a smaller triangular number.

1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 2, 2, 3, 3, 3, 4, 2, 3, 2, 5, 4, 5, 5, 3, 4, 4, 3, 2, 3, 6, 5, 4, 5, 5, 7, 4, 6, 5, 4, 8, 5, 6, 9, 10, 4, 3, 5, 9, 9, 10, 9, 9, 10, 7, 6, 7, 4, 10, 9, 7, 11, 7, 8, 12, 14, 7, 11, 12, 9, 13, 9, 12, 9, 9, 15, 16, 12, 11, 16, 15, 11, 8, 11, 8

Offset

0,13

Comments

Same as A109037 except at triangular indices. Conjecture than lim_{n->\inf} a(n) = \inf.

Links

Table of n, a(n) for n=0..94.

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, A109037.

Sequence in context: A273165 A336313 A095139 * A208246 A320857 A211664

Adjacent sequences: A109035 A109036 A109037 * A109039 A109040 A109041

Keyword

nonn

Author

Franklin T. Adams-Watters, Jun 16 2005

Status

approved