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A109035
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Number of irreducible partitions into squares. A partition is irreducible if no subpartition with 2 or more parts sums to a square.
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2
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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; internal format)
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OFFSET
| 0,13
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COMMENTS
| Sequence is unbounded, as can be seen by considering sums of 2 squares (thanks to David 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.
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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.
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CROSSREFS
| Cf: A001156, A109036.
Sequence in context: A025887 A025882 A025876 * A064823 A140225 A104758
Adjacent sequences: A109032 A109033 A109034 * A109036 A109037 A109038
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KEYWORD
| nonn
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AUTHOR
| Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jun 16 2005
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