Search: id:A158118
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%I A158118
%S A158118 0,0,0,0,0,0,0,0,0,0,0,2,0,0,4,2,0,0,4,124,0,0,536,712,0,0,4574,2260,0,
%T A158118 0,10634,73758,0,0,406032,638830,0,0,4249160,3263500,0,0,21907736,
%U A158118 82561050,0,0,485798436,945916970,0,0,5968541478,6839493576,0,0
%N A158118 Number of solutions of +-1+-2^3+-3^3..+-n^3=0.
%C A158118 Constant term in the expansion of (x + 1/x)(x^8 + 1/x^8)..(x^n^3 + 1/
               x^n^3).
%C A158118 a(n)=0 for any n=1 (mod4) or n=2 (mod4).
%F A158118 Integral representation:
%F A158118 a(n)=((2^n)/pi)*int_0^pi prod_{k=1}^n cos(x*k^3) dx
%F A158118 Asymptotic formula:
%F A158118 a(n)=(2^n)*sqrt(14/(pi*n^7))*(1+o(1)) as n-->infty; n=-1 or 0 (mod 4).
%e A158118 Example: For n=12 the a(12)=2 solutions are: +1+8-27+64-125-216-343+512+729-1000-1331+1728=0 
               -1-8+27-64+125+216+343-512-729+1000+1331-1728=0
%p A158118 N:=60: p:=1: a:=[]: for n from 1 to N do p:=expand(p*( x^(n^3) + x^(-n^3) 
               )): a:=[op(a), coeff(p,x,0)]: od:a;
%Y A158118 A063865
%Y A158118 A158092, A019568 [From Pietro Majer (majer(AT)dm.unipi.it), Mar 15 2009]
%Y A158118 Sequence in context: A106235 A118965 A121552 this_sequence A147592 A108885 
               A072740
%Y A158118 Adjacent sequences: A158115 A158116 A158117 this_sequence A158119 A158120 
               A158121
%K A158118 nonn
%O A158118 1,12
%A A158118 Pietro Majer (majer(AT)dm.unipi.it), Mar 12 2009

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