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

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

Author

Reinhard Zumkeller, Aug 10 2007

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A000009, A132015.

Formula

a(n) = f(n,1) with f(m,p) = if p=m then 1 else (if p

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