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Search: id:A132085
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| A132085 |
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Number of partitions of n into distinct parts such that (u+1)^2 <= v for all pairs (u,v) of parts with u<v. |
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+0
5
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| 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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A132086, A132087, and A132088 give record values and where and how often they occur.
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LINKS
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R. Zumkeller, Table of n, a(n) for n = 1..10000
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FORMULA
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a(n) = f(n,1) with f(m,p) = if p=m then 1 else (if p<m then f(m-1,(p+1)^2)+f(m,p+1) else 0).
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EXAMPLE
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a(10)=#{10,9+1}=2;
a(20)=#{20,19+1,18+2,17+3}=4;
a(30)=#{30,29+1,28+2,27+3,26+4,25+4+1}=6;
a(40)=#{40,39+1,38+2,37+3,36+4,35+4+1}=6;
a(50)=#{50,49+1,48+2,47+3,46+4,45+5,45+4+1,44+5+1}=8;
a(60)=#{60,59+1,58+2,57+3,56+4,55+5,55+4+1,54+6,54+5+1,53+6+1}=10.
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CROSSREFS
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Cf. A000009, A132015.
Sequence in context: A056556 A111651 A111854 this_sequence A111654 A067099 A098429
Adjacent sequences: A132082 A132083 A132084 this_sequence A132086 A132087 A132088
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 10 2007
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