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A100088
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Expansion of (1-x^2)/((1-2x)(1+x^2)).
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3
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1, 2, 2, 4, 10, 20, 38, 76, 154, 308, 614, 1228, 2458, 4916, 9830, 19660, 39322, 78644, 157286, 314572, 629146, 1258292, 2516582, 5033164, 10066330, 20132660, 40265318, 80530636, 161061274, 322122548, 644245094, 1288490188, 2576980378
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| A Chebyshev transform of A100087, under the mapping A(x)->((1-x^2)/(1+x^2))A(x/(1+x^2)).
A176742(n+2)=A084099(n+2)=period 4:repeat 0,-2,0,2.
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LINKS
| Index entries for sequences related to linear recurrences with constant coefficients, signature (2,-1,2).
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FORMULA
| a(n)=(3*2^n+2cos(pi*n/2)+4sin(pi*n/2))/5; a(n)=n*sum{k=0..floor(n/2), binomial(n-k, k)(-1)^k*A100087(n-2k)/(n-k)}.
a(0)=1; a(n)=2*a(n-1)+period 4:repeat 0,-2,0,2.
A007910(n-1)=0,0,1,2,3,6,13,26,51,102.
a(n)=A007910(n+1)-A007910(n-1).
a(n) = 2a(n-1) - a(n-2) + 2a(n-3).
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MATHEMATICA
| CoefficientList[Series[(1-x^2)/((1-2x)(1+x^2)), {x, 0, 40}], x] (* or *) LinearRecurrence[{2, -1, 2}, {1, 2, 2}, 40] (* From Harvey P. Dale, May 12 2011 *)
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CROSSREFS
| Sequence in context: A002082 A005304 A152732 * A025244 A132824 A078801
Adjacent sequences: A100085 A100086 A100087 * A100089 A100090 A100091
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Nov 03 2004
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