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A109036
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Number of irreducible partitions into smaller squares. A partition is irreducible if no subpartition with 2 or more parts sums to a square smaller than n.
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1
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1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 2, 2, 3, 2, 2, 2, 1, 2, 2, 3, 2, 3, 2, 3, 3, 2, 3, 3, 2, 2, 3, 1, 2, 3, 3, 3, 2, 3, 3, 5, 3, 2, 3, 4, 4, 4, 5, 5, 6, 4, 4, 5, 3, 3, 4, 7, 3, 5, 6, 6, 7, 7, 7, 6, 6, 3, 5, 7, 8, 7, 8, 7, 9, 4, 5, 9, 5, 5, 6, 10, 4, 6, 9, 11, 11, 10, 10, 11, 8, 7, 6, 7, 7
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,13
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COMMENTS
| This is the same as A109035 except for the values at squares. Conjecture that lim_{n->\inf} a(n) = \inf.
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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: A109035, A001156.
Sequence in context: A095407 A038605 A113121 * A085031 A029342 A029408
Adjacent sequences: A109033 A109034 A109035 * A109037 A109038 A109039
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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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