A132085 Number of partitions of n into distinct parts such that (u+1)^2 <= v for all pairs (u,v) of parts with u<v.

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

Offset

1,5

Comments

A132086, A132087 and A132088 give record values and where and how often they occur.

Links

R. Zumkeller, Table of n, a(n) for n = 1..10000

Formula

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).

Example

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.

Crossrefs

Cf. A000009, A132015.

Sequence in context: A151982 A259361 A111854 * A111654 A264749 A240567

Adjacent sequences: A132082 A132083 A132084 * A132086 A132087 A132088

Keyword

nonn

Author

Reinhard Zumkeller, Aug 10 2007

Status

approved