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A109037
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Number of irreducible partitions into triangular numbers. A partition is irreducible if no subpartition with 2 or more parts sums to a triangular number.
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1
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 2, 2, 3, 3, 3, 1, 2, 3, 3, 3, 4, 2, 1, 2, 5, 4, 5, 5, 3, 4, 1, 3, 2, 3, 6, 5, 4, 5, 5, 1, 4, 6, 5, 4, 8, 5, 6, 9, 10, 1, 3, 5, 9, 9, 10, 9, 9, 10, 7, 6, 1, 4, 10, 9, 7, 11, 7, 8, 12, 14, 7, 11, 1, 9, 13, 9, 12, 9, 9, 15, 16, 12, 11, 16, 15, 1, 8, 11, 8, 16
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,13
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COMMENTS
| Sequence is almosot certainly unbounded. Obviously it contains infinitely many 1's, at triangular indices. At non-triangular 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(9)=1 for the partition [6,3]. [6,1^3], [3^3], [3^2,1^3], [3,1^6] and [1^9] are all excluded because they contain subpartitions [3^2] or [1^3] summing to a triangular number.
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CROSSREFS
| Cf: A007294, A109038, A109035.
Sequence in context: A106493 A083338 A204018 * A147680 A192895 A120965
Adjacent sequences: A109034 A109035 A109036 * A109038 A109039 A109040
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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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