A132015 - OEIS

%I #4 Mar 30 2012 18:50:58

%S 1,1,2,2,2,2,3,4,4,4,4,4,5,6,6,6,6,6,6,6,7,8,8,8,8,8,8,8,8,8,9,10,11,

%T 12,12,12,12,12,12,12,12,12,13,14,15,16,16,16,16,16,16,16,16,16,16,16,

%U 17,18,19,20,20,20,20,20,20,20,20,20,20,20,20,20,21,22,23,24,24,24,24,24

%N Number of partitions of n into distinct parts such that u^2 < v for all pairs (u,v) of parts with u<v.

%C A132016, A132017 and A132042 give record values and where and how often they occur.

%H R. Zumkeller, <a href="/A132015/b132015.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = f(n,1) with f(m,p) = if p=m then 1 else (if p<m then f(m-1,1+p^2)+f(m,p+1) else 0)."

%e a(10) = #{10, 9+1, 8+2, 7+2+1} = 4;

%e a(11) = #{11, 10+1, 9+2, 8+2+1} = 4;

%e a(12) = #{12, 11+1, 10+2, 9+2+1} = 4;

%e a(13) = #{13, 12+1, 11+2, 10+3, 10+2+1} = 5;

%e a(14) = #{14, 13+1, 12+2, 11+3, 11+2+1, 10+3+1} = 6;

%e a(15) = #{15, 14+1, 13+2, 12+3, 12+2+1, 11+3+1} = 6.

%Y Cf. A000009, A132011.

%Y Cf. A132085.

%K nonn

%O 1,3

%A _Reinhard Zumkeller_, Aug 08 2007