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A086674 Sum of signed indices from Euler's Pentagonal Theorem (see A000041). 0


%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))*(n-k)}

%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+8-5-3=9.

%o (PARI) { gp=vecsort(vector(20,i,x=10-i; x*(3*x-1)/2)); for (n=1,50,s=0; i=1; while (n-gp[i+1]>0, s-=(-1)^(floor((i+1)/2))*(n-gp[i+1]); i++); print1(","s)) }

%Y Cf. A001318 (GP's), A000041 (partition function).

%K nonn

%O 1,3

%A _Jon Perry_, Sep 12 2003

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Last modified September 30 11:58 EDT 2022. Contains 357105 sequences. (Running on oeis4.)