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A046978
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Numerators of Taylor series for exp(x)*sin(x).
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11
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0, 1, 1, 1, 0, -1, -1, -1, 0, 1, 1, 1, 0, -1, -1, -1, 0, 1, 1, 1, 0, -1, -1, -1, 0, 1, 1, 1, 0, -1, -1, -1, 0, 1, 1, 1, 0, -1, -1, -1, 0, 1, 1, 1, 0, -1, -1, -1, 0, 1, 1, 1, 0, -1, -1, -1, 0, 1, 1, 1, 0, -1, -1, -1, 0, 1, 1, 1, 0, -1, -1, -1, 0, 1, 1, 1, 0, -1, -1, -1, 0, 1, 1, 1, 0, -1, -1, -1, 0, 1, 1, 1, 0, -1, -1, -1, 0, 1, 1, 1, 0, -1, -1, -1, 0
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OFFSET
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0,1
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COMMENTS
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Period 8: repeat [0, 1, 1, 1, 0, -1, -1, -1].
This is a strong elliptic divisibility sequence t_n as given in [Kimberling, p. 16] where x = 1, y = 1, z = 0. - Michael Somos, Nov 27 2019
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REFERENCES
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G. W. Caunt, Infinitesimal Calculus, Oxford Univ. Press, 1914, p. 477.
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LINKS
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FORMULA
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Euler transform of length 8 sequence [1, 0, -1, -1, 0, 0, 0, 1]. - Michael Somos, Jul 16 2006
G.f.: x * (1 + x + x^2) / (1 + x^4) = x * (1 - x^3) * (1 - x^4) / ((1 - x) * (1 - x^8)). a(-n) = a(n + 4) = -a(n). - Michael Somos, Jul 16 2006
a(n) = round((b^n - c^n)/(b - c)) where b = sqrt(2)-((1+i)/sqrt(2)), c = (1+i)/sqrt(2). - Artur Jasinski, Oct 06 2008
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EXAMPLE
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G.f. = x + x^2 + x^3 - x^5 - x^6 - x^7 + x^9 + x^10 + x^11 - x^13 - x^14 - ...
1*x + 1*x^2 + (1/3)*x^3 - (1/30)*x^5 - (1/90)*x^6 - (1/630)*x^7 + (1/22680)*x^9 + (1/113400)*x^10 + ...
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MAPLE
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MATHEMATICA
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a = -((1 + I)/Sqrt[2]) + Sqrt[2]; b = (1 + I)/Sqrt[2]; Table[ Round[(a^n - b^n)/(a - b)], {n, 0, 200}] (* Artur Jasinski, Oct 06 2008 *)
LinearRecurrence[{0, 0, 0, -1}, {0, 1, 1, 1}, 120] (* or *) PadRight[{}, 120, {0, 1, 1, 1, 0, -1, -1, -1}] (* Harvey P. Dale, Mar 17 2017 *)
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PROG
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(PARI) {a(n) = (n%4 > 0) * (-1)^(n\4)}; /* Michael Somos, Jul 16 2006 */
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CROSSREFS
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KEYWORD
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sign,frac,easy
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AUTHOR
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STATUS
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approved
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