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Search: id:A009116
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| A009116 |
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Expansion of cos(x)/exp(x). |
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+0
18
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| 1, -1, 0, 2, -4, 4, 0, -8, 16, -16, 0, 32, -64, 64, 0, -128, 256, -256, 0, 512, -1024, 1024, 0, -2048, 4096, -4096, 0, 8192, -16384, 16384, 0, -32768, 65536, -65536, 0, 131072, -262144, 262144, 0, -524288, 1048576, -1048576, 0, 2097152, -4194304
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Apart from signs, generated by 1,1 position of H_2^n=[1,1;-1,1]^n; and a(n)=2^(n/2)cos(pi*n/2) - Paul Barry (pbarry(AT)wit.ie), Feb 18 2004
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FORMULA
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Real part of (-1-i)^n - Marc LeBrun (mlb(AT)well.com)
a(n)=-2*(a(n-1)+a(n-2)), a(0)=1, a(1)=-1 - Michael Somos
Sum_{j=0..[n/2]} (-1)^j*binomial(n, 2*j).
G.f.: (1+x)/(1+2x+2x^2). E.g.f.: cos(x)/exp(x).
a(n)= Sum_{k, 0<=k<=n}(-1)^k*A098158(n,k) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 04 2006
a(n)*(-1)^n=A099087(n)-A099087(n-1). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 18 2007
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MAPLE
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A009116 := n->add((-1)^j*binomial(n, 2*j), j=0..floor(n/2));
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MATHEMATICA
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Cos[ x ]/Exp[ x ]
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PROGRAM
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(PARI) a(n)=if(n<0, 0, polcoeff((1+x)/(1+2*x+2*x^2)+x*O(x^n), n))
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CROSSREFS
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Cf. A009545.
Cf. A090132.
(With different signs) Row sums of triangle A104597.
Adjacent sequences: A009113 A009114 A009115 this_sequence A009117 A009118 A009119
Sequence in context: A053124 A071970 A111172 this_sequence A118434 A090132 A099211
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KEYWORD
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sign,easy,nice
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AUTHOR
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R. H. Hardin (rhh(AT)cadence.com)
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EXTENSIONS
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Extended with signs Mar 15 1997 by Olivier Gerard.
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