cp's OEIS Frontend

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

%I A132085 #4 Mar 30 2012 18:50:58
%S A132085 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,
%T A132085 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,
%U A132085 10,10,10,10,10,10,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12
%N 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.
%C A132085 A132086, A132087 and A132088 give record values and where and how often they occur.
%H A132085 R. Zumkeller, <a href="/A132085/b132085.txt">Table of n, a(n) for n = 1..10000</a>
%F A132085 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).
%e A132085 a(10)=#{10,9+1}=2;
%e A132085 a(20)=#{20,19+1,18+2,17+3}=4;
%e A132085 a(30)=#{30,29+1,28+2,27+3,26+4,25+4+1}=6;
%e A132085 a(40)=#{40,39+1,38+2,37+3,36+4,35+4+1}=6;
%e A132085 a(50)=#{50,49+1,48+2,47+3,46+4,45+5,45+4+1,44+5+1}=8;
%e A132085 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.
%Y A132085 Cf. A000009, A132015.
%K A132085 nonn
%O A132085 1,5
%A A132085 _Reinhard Zumkeller_, Aug 10 2007