id:A109036 - OEIS Search Results

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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.

+0
2

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; listen)

	OFFSET	`0,13`
	COMMENT	`This is the same as A109035 except for the values at squares. Conjecture that lim_{n->\inf} a(n) = \inf.`
	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: A109035, A001156.` `Sequence in context: A095407 A038605 A113121 this_sequence A085031 A029342 A029408` `Adjacent sequences: A109033 A109034 A109035 this_sequence A109037 A109038 A109039`
	KEYWORD	`nonn`
	AUTHOR	`Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jun 16 2005`

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Last modified August 29 17:54 EDT 2008. Contains 143238 sequences.

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