A109035 Number of irreducible partitions into squares. A partition is irreducible if no subpartition with 2 or more parts sums to a square.

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

Offset

0,13

Comments

Sequence is unbounded, as can be seen by considering sums of 2 squares (thanks to David L. Harden). Obviously it contains infinitely many 1's, at square indices. At nonsquare 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..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. A001156, A109036.

Sequence in context: A025887 A025882 A025876 * A244231 A237706 A064823

Adjacent sequences: A109032 A109033 A109034 * A109036 A109037 A109038

Keyword

nonn

Author

Franklin T. Adams-Watters, Jun 16 2005

Status

approved