|
%I #8 Aug 26 2024 02:07:09
%S 1,2,4,5,7,8,10,10,12,14,16,17,18,19,22,23,24,25,26,27,29,31,32,34,36,
%T 37,38,39,41,42,44,45,47,48,49,50,53,54,55,56,57,58,61,62,65,66,67,68,
%U 69,71,72,73,74,77,78,79,81,83,84,85,86,87,89,91,93,94,95,96,97,98
%N Number of triangles of partition numbers with the n-partition number as largest side.
%C a(n) = #{(i,j): 1<=i<=j<=n and P(n)<=P(i)+P(j)}, P=A000041.
%e a(10)=14: P(10)=42 and
%e 42<=P(10)+P(10)=42+42,42<=P(10)+P(9)=42+30, 42<=P(10)+P(8)=42+22,
%e 42<=P(10)+P(7)=42+15, 42<=P(10)+P(6)=42+11, 42<=P(10)+P(5)=42+7,
%e 42<=P(10)+P(4)=42+5, 42<=P(10)+P(3)=42+3, 42<=P(10)+P(2)=42+2,
%e 42<=P(10)+P(1)=42+1, 42<=P(9)+P(9)=30+30, 42<=P(9)+P(8)=30+22,
%e 42<=P(9)+P(7)=30+15 and 42<=P(8)+P(8)=22+22.
%K nonn
%O 1,2
%A _Reinhard Zumkeller_, Feb 06 2004
|
