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 A109035 Number of irreducible partitions into squares. A partition is irreducible if no subpartition with 2 or more parts sums to a square. 2
 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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified July 31 14:49 EDT 2021. Contains 346374 sequences. (Running on oeis4.)