%I
%S 0,1,3,5,7,8,9,9,9,9,9,9,10,11,12,14,16,18,20,22,24,26,27,28,29,30,30,
%T 30,30,30,30,30,30,30,30,31,32,33,34,35,37,39,41,43,45,47,49,51,53,55
%N Sum of signed indices from Euler's Pentagonal Theorem (see A000041).
%C Is the sequence increasing? (checked to n=5000).
%F a(n)=sum{k_i is a generalized pentagonal, (1)^(floor((i+1)/2))*(nk)}
%e a(10) is given via the expansion part(10)=part(9)+part(8)part(5)part(3), so in this sequence a(10)=9+853=9.
%o (PARI) { gp=vecsort(vector(20,i,x=10i; x*(3*x1)/2)); for (n=1,50,s=0; i=1; while (ngp[i+1]>0, s=(1)^(floor((i+1)/2))*(ngp[i+1]); i++); print1(","s)) }
%Y Cf. A001318 (GP's), A000041 (partition function).
%K nonn
%O 1,3
%A _Jon Perry_, Sep 12 2003
