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A143064
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Expansion of a Ramanujan false theta series variation of A089801 in powers of x.
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1
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1, 1, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 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, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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REFERENCES
| S. Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, p. 41
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FORMULA
| a(n) = b(3n + 1) where b(n) is multiplicative and b(p^(2e)) = (-1)^e if p = 5 (mod 6), b(p^(2e)) = +1 if p = 1 (mod 6) and b(p^(2e-1)) = b(2^e) = b(3^e) = 0 if e>0.
a(4*n + 2) = a(4*n + 3) = a(8*n + 4) = 0.
G.f.: Sum_{k>=0} (-1)^k * x^(3*k^2 + 2*k) * ( 1 + x^(2*k+1) ).
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EXAMPLE
| q + q^4 - q^16 - q^25 + q^49 + q^64 - q^100 - q^121 + q^169 + q^196 + ...
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PROG
| (PARI) {a(n) = if( issquare( 3*n + 1, &n), (-1)^(n \ 3) )}
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CROSSREFS
| Cf. A143062(n) = a(8*n). Convolution of A010054 with A143065.
Sequence in context: A089802 * A185124 A185125 A163811 A163817 A151667
Adjacent sequences: A143061 A143062 A143063 * A143065 A143066 A143067
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KEYWORD
| sign
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AUTHOR
| Michael Somos, Jul 21 2008
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