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A084099
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Expansion of (1+x)^2/(1+x^2).
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7
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1, 2, 0, -2, 0, 2, 0, -2, 0, 2, 0, -2, 0, 2, 0, -2, 0, 2, 0, -2, 0, 2, 0, -2, 0, 2, 0, -2, 0, 2, 0, -2, 0, 2, 0, -2, 0, 2, 0, -2, 0, 2, 0, -2, 0, 2, 0, -2, 0, 2, 0, -2, 0, 2, 0, -2, 0, 2, 0, -2, 0, 2, 0, -2, 0, 2, 0, -2, 0, 2, 0, -2, 0, 2, 0, -2, 0, 2, 0, -2, 0, 2, 0, -2, 0, 2, 0, -2, 0, 2, 0, -2, 0, 2, 0, -2, 0, 2, 0, -2, 0, 2, 0, -2, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Inverse binomial transform of A077860. Partial sums of A084100.
Transform of sqrt(1+2x)/sqrt(1-2x) (A063886) under the Chebyshev transformation A(x)->((1-x^2)/(1+x^2))A(x/(1+x^2)). - Paul Barry (pbarry(AT)wit.ie), Oct 12 2004
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FORMULA
| Euler transform of length 4 sequence [ 2, -3, 0, 1]. - Michael Somos Aug 04 2009
a(n+2)=(-1)^[A180969(1,n)]*[(-1)^n - 1]
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EXAMPLE
| 1 + 2*x - 2*x^3 + 2*x^5 - 2*x^7 + 2*x^9 - 2*x^11 + 2*x^13 - 2*x^15 + ...
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MATHEMATICA
| CoefficientList[Series[(1+x)^2/(1+x^2), {x, 0, 110}], x] (* or *) Join[ {1}, PadRight[{}, 120, {2, 0, -2, 0}]] (* From Harvey P. Dale, Nov 23 2011 *)
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PROG
| (PARI) {a(n) = if( n<1, n==0, 2 * if(n%2, (-1)^(n\2)) )} /* Michael Somos Aug 04 2009 */
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CROSSREFS
| 2 * A101455(n) = a(n) unless n=0.
Sequence in context: A021499 A176742 A010673 * A036665 A053472 A036664
Adjacent sequences: A084096 A084097 A084098 * A084100 A084101 A084102
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KEYWORD
| easy,sign
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), May 15 2003
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