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Search: id:A099087
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| 1, 2, 2, 0, -4, -8, -8, 0, 16, 32, 32, 0, -64, -128, -128, 0, 256, 512, 512, 0, -1024, -2048, -2048, 0, 4096, 8192, 8192, 0, -16384, -32768, -32768, 0, 65536, 131072, 131072, 0, -262144, -524288, -524288, 0, 1048576, 2097152, 2097152, 0, -4194304, -8388608, -8388608, 0, 16777216
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Yet another variation on A009545.
Row sums of Krawtchouk triangle A098593. Partial sums of e.g.f. exp(x)cos(x), or 2^(n/2)cos(pi*n/2). See A009116.
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FORMULA
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E.g.f.: exp(x)(cos(x)+sin(x)); a(n)=2^(n/2)(cos(pi*n/4)+sin(pi*n/4)); a(n)=sum{k=0..n, sum{i=0..k, C(n-k, k-i)C(n, i)(-1)^(k-i)}}; a(n)=2a(n-1)-2a(n-2).
a(n) = (1-I)^(n-1)+(1+I)^(n-1) where I=sqrt(-1). a(n) = 2 sum_{k=0,1,2,..(n-1)/2} (-1)^k*binomial(n-1,2k) if n>0. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 18 2008
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CROSSREFS
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Cf. A009545.
Adjacent sequences: A099084 A099085 A099086 this_sequence A099088 A099089 A099090
Sequence in context: A100240 A072690 A108520 this_sequence A009545 A084102 A052079
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KEYWORD
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easy,sign,new
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Sep 24 2004
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EXTENSIONS
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Signs added by njas, Nov 14, 2006
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