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 A113414 Expansion of Sum_{k>0} x^k/(1-(-x^2)^k). 2
 1, 1, 0, 1, 2, 2, 0, 1, 1, 2, 0, 2, 2, 2, 0, 1, 2, 3, 0, 2, 0, 2, 0, 2, 3, 2, 0, 2, 2, 4, 0, 1, 0, 2, 0, 3, 2, 2, 0, 2, 2, 4, 0, 2, 2, 2, 0, 2, 1, 3, 0, 2, 2, 4, 0, 2, 0, 2, 0, 4, 2, 2, 0, 1, 4, 4, 0, 2, 0, 4, 0, 3, 2, 2, 0, 2, 0, 4, 0, 2, 1, 2, 0, 4, 4, 2, 0, 2, 2, 6, 0, 2, 0, 2, 0, 2, 2, 3, 0, 3, 2, 4, 0, 2, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 LINKS FORMULA Moebius transform is period 8 sequence [1, 0, -1, 0, 1, 2, -1, 0, ...]. G.f.: Sum_{k>0} x^k/(1-(-x^2)^k) = Sum_{k>0} x^k/(1+x^(2k))+2x^(6k)/(1-x^(8k)) = Sum_{k>0} -(-1)^k x^(2k-1)/(1+(-1)^k*x^(2k-1)). a(4n+3) = 0. a(n) = A001826(n) + (-1)^n * A001842(n). - David Spies, Sep 26 2012 PROG (PARI) a(n)=if(n<1, 0, sumdiv(n, d, kronecker(-4, d)+2*(n%2==0)*(d%4==3))) (PARI) {a(n)=if(n<1, 0, if(n%4==3, 0, if(n%4==2, numdiv(n/2), if(n%4==0, sumdiv(n, d, d%2), sumdiv(n, d, (-1)^(d\2))))))} (PARI) {a(n)=if(n<1, 0, polcoeff( sum(k=1, sqrtint(8*n+1)\2, (-1)^(k%4==2)*x^((k^2+k)/2)/(1-(-1)^(k\2)*x^k), x*O(x^n)), n))} (PARI) {a(n)=if(n<1, 0, polcoeff( sum(k=1, n, x^k/(1-(-x^2)^k), x*O(x^n)), n))} CROSSREFS A001227(n) = a(2*n), A008441(n) = a(4*n+1), A099774(n) = a(4*n+2). Sequence in context: A270740 A189463 A287451 * A286653 A283308 A255636 Adjacent sequences:  A113411 A113412 A113413 * A113415 A113416 A113417 KEYWORD nonn AUTHOR Michael Somos, Oct 29 2005 STATUS approved

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Last modified January 16 21:37 EST 2019. Contains 319206 sequences. (Running on oeis4.)