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A214505
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a(n) = 1 if n is four times a triangular number, -1 if one more than twelve times a triangular number else 0.
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2
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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
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OFFSET
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0,1
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COMMENTS
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LINKS
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FORMULA
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Expansion of psi(x^4) - x * psi(x^12) in powers of x where psi() is a Ramanujan theta function.
Expansion of f(-x, x^5) * f(-x^4, -x^8) / f(x, -x) in powers of x where f(,) is the Ramanujan two-variable theta function.
Euler transform of period 24 sequence [ -1, 0, 0, 1, 1, 1, 1, 0, 0, -1, -1, -1, -1, -1, 0, 0, 1, 1, 1, 1, 0, 0, -1, -1, ...].
G.f.: (Sum_{k} x^(2*k*(k + 1)) - x^(6*k*(k + 1) + 1)) / 2.
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EXAMPLE
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1 - x + x^4 + x^12 - x^13 + x^24 - x^37 + x^40 + x^60 - x^73 + x^84 + ...
q - q^3 + q^9 + q^25 - q^27 + q^49 - q^75 + q^81 + q^121 - q^147 + q^169 + ...
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PROG
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(PARI) {a(n) = n = 2*n + 1; issquare(n) - issquare(3*n)}
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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