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Search: id:A113414
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| A113414 |
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Expansion of Sum_{k>0} x^k/(1-(-x^2)^k). |
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+0
3
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| 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; listen)
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OFFSET
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1,5
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FORMULA
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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.
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PROGRAM
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(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))}
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CROSSREFS
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A001227(n) = a(2*n), A008441(n) = a(4*n+1), A099774(n) = a(4*n+2).
Sequence in context: A124407 A137581 A156311 this_sequence A112185 A112555 A108561
Adjacent sequences: A113411 A113412 A113413 this_sequence A113415 A113416 A113417
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Oct 29 2005
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