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Search: id:A133100
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| A133100 |
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Expansion of f(x, x^4) in powers of x where f() is Ramanujan's two variable theta function. |
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+0
1
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| 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 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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The characteristic function of A085787 generalized heptagonal numbers.
Euler transform of period 10 sequence [ 1, -1, 0, 1, -1, 1, 0, -1, 1, -1, ...].
G.f.: Prod_{k>0} (1-x^(5k)) * (1+x^(5k-1)) * (1+x^(5k-4)) = Sum_{k} x^((5*k^2 + 3*k) / 2).
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EXAMPLE
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1 + q + q^4 + q^7 + q^13 + q^18 + q^27 + q^34 + q^46 + q^55 + q^70 + ...
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PROGRAM
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(PARI) {a(n) = if( n<0, 0, polcoeff( prod(k=1, n, 1 + x^k*[ -1, 1, 0, 0, 1][k%5+1], 1+x*O(x^n)), n))}
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CROSSREFS
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|A113429(n)| = a(n).
Sequence in context: A087049 A118009 A113429 this_sequence A077606 A004601 A114915
Adjacent sequences: A133097 A133098 A133099 this_sequence A133101 A133102 A133103
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Sep 11 2007
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