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Search: id:A083023
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| A083023 |
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a(n) = number of partitions of n into pair of parts n=p+q, p>=q>=0, with p-q equal to a square >= 0. |
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+0
2
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| 1, 1, 1, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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Number of integers k, 0 <= k <= n/2 such that n - 2k is a square.
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FORMULA
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See Maple line.
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EXAMPLE
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a(11) = 2: the partitions are (1,10) and (5,6).
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MAPLE
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f := n->if n mod 2 = 0 then floor(sqrt((n-2)/4))+1 else floor(sqrt((n-2)/4)-1/2)+1; fi; # then add 1 if n is a square!
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CROSSREFS
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See A084359 for another version.
Adjacent sequences: A083020 A083021 A083022 this_sequence A083024 A083025 A083026
Sequence in context: A048684 A109969 A085035 this_sequence A084359 A143935 A008616
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KEYWORD
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nonn,easy
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AUTHOR
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Anne M. Donovan (anned3005(AT)aol.com) May 31 2003
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EXTENSIONS
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More terms from Michel ten Voorde (seqfan(AT)tenvoorde.org) Jun 13 2003
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