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Search: id:A143433
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| A143433 |
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Expansion of f(-x, x^3) in powers of x where f(,) is Ramanujan's two variable theta function. |
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+0
2
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| 1, -1, 0, 1, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 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, 0, 0, 0
(list; graph; listen)
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OFFSET
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0,1
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FORMULA
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Euler transform of period 16 sequence [ -1, 0, 1, 1, 1, -1, -1, -2, -1, -1, 1, 1, 1, 0, -1, -1, ...].
Pattern of signs of nonzero terms is A143431.
G.f.: Sum_{k>=0} (-1)^(k + k\4) * x^(k * (k+1) / 2).
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EXAMPLE
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q - q^9 + q^25 - q^49 - q^81 + q^121 - q^169 + q^225 + q^289 - q^361 + ...
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PROGRAM
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(PARI) {a(n) = if( n<0, 0, if(issquare(8*n + 1, &n), n = n\2; (-1)^(n + n\4), 0))}
(PARI) {a(n) = local(A); if( n<0, 0, polcoeff( prod(k=1, n, (1 - x^k)^( [1, 1, 0, -1, -1, -1, 1, 1, 2, 1, 1, -1, -1, -1, 0, 1, 1] [k%16 + 1]), 1 + x * O(x^n)), n))}
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CROSSREFS
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(-1)^n * A143434(n) = a(n).
Sequence in context: A155972 A010054 A106459 this_sequence A143434 A033806 A033802
Adjacent sequences: A143430 A143431 A143432 this_sequence A143434 A143435 A143436
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Aug 14 2008
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