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Search: id:A127692
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| A127692 |
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Expansion of psi(x^4)+x*psi(x^12) in powers of x where psi() is a Ramanujan theta function. |
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1
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| 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
(list; graph; listen)
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OFFSET
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0,1
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REFERENCES
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R. Blecksmith; J. Brillhart; I. Gerst, Some infinite product identities, Math. Comp. 51 (1988), no. 183, 301-314. MR0942157 (89f:05017)
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FORMULA
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Euler transform of period 24 sequence [ 1, -1, 0, 1, -1, 1, -1, 0, 0, 0, 1, -1, 1, 0, 0, 0, -1, 1, -1, 1, 0, -1, 1, -1, ...].
a(n)=b(2n+1) where b(n) is multiplicative and b(2^e)=0^e, b(3^e)=1, else b(p^e)=(1+(-1)^e)/2.
a(3n+1)=a(n), a(3n+2)=a(4n+2)=a(4n+3)=a(6n+3)=0.
G.f.: Sum_{k>0} x^(2k(k-1)) +x^(6k(k-1)+1) = Product_{k>0} (1-x^(24k)) (1-x^(24k-5)) (1-x^(24k-7)) (1-x^(24k-17)) (1-x^(24k-19)) (1+x^(12k-1)) (1+x^(12k-4)) (1+x^(12k-6)) (1+x^(12k-8)) (1+x^(12k-11)).
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PROGRAM
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(PARI) {a(n)=issquare(2*n+1)+issquare(6*n+3)}
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CROSSREFS
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Cf. A005369(n)=a(2n). A010054(n)=a(4n). A089806(n)=a(6n). A080995(n)=a(12n).
Sequence in context: A016039 A138149 A113047 this_sequence A023533 A010052 A039985
Adjacent sequences: A127689 A127690 A127691 this_sequence A127693 A127694 A127695
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Jan 19 2007
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