Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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