A109036 Number of irreducible partitions into smaller squares. A partition is irreducible if no subpartition with 2 or more parts sums to a square smaller than n.

1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 2, 2, 3, 2, 2, 2, 1, 2, 2, 3, 2, 3, 2, 3, 3, 2, 3, 3, 2, 2, 3, 1, 2, 3, 3, 3, 2, 3, 3, 5, 3, 2, 3, 4, 4, 4, 5, 5, 6, 4, 4, 5, 3, 3, 4, 7, 3, 5, 6, 6, 7, 7, 7, 6, 6, 3, 5, 7, 8, 7, 8, 7, 9, 4, 5, 9, 5, 5, 6, 10, 4, 6, 9, 11, 11, 10, 10, 11, 8, 7, 6, 7, 7

Offset

0,13

Comments

This is the same as A109035 except for the values at squares. Conjecture that lim_{n->oo} a(n) = oo.

Links

Table of n, a(n) for n=0..101.

Example

a(10)=1 for the partition [9,1]. [4^2,1^2], [4,1^6] and [1^10] are all excluded because they contain subpartitions [4^2,1] or [1^4] summing to a square.

Crossrefs

Cf. A109035, A001156.

Sequence in context: A095407 A038605 A113121 * A085031 A341974 A029342

Adjacent sequences: A109033 A109034 A109035 * A109037 A109038 A109039

Keyword

nonn

Author

Franklin T. Adams-Watters, Jun 16 2005

Status

approved