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Search: id:A109035
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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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3
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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
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OFFSET
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0,13
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COMMENT
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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 non-square 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
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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
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Cf: A001156, A109036.
Sequence in context: A025887 A025882 A025876 this_sequence A064823 A140225 A104758
Adjacent sequences: A109032 A109033 A109034 this_sequence A109036 A109037 A109038
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KEYWORD
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nonn
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AUTHOR
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Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jun 16 2005
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