Search: id:A099087
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%I A099087
%S A099087 1,2,2,0,4,8,8,0,16,32,32,0,64,128,128,0,256,512,512,0,1024,2048,2048,
               0,
%T A099087 4096,8192,8192,0,16384,32768,32768,0,65536,131072,131072,0,262144,524288,
%U A099087 524288,0,1048576,2097152,2097152,0,4194304,8388608,8388608,0,16777216
%V A099087 1,2,2,0,-4,-8,-8,0,16,32,32,0,-64,-128,-128,0,256,512,512,0,-1024,-2048,
               -2048,0,
%W A099087 4096,8192,8192,0,-16384,-32768,-32768,0,65536,131072,131072,0,-262144,
               -524288,
%X A099087 -524288,0,1048576,2097152,2097152,0,-4194304,-8388608,-8388608,0,16777216
%N A099087 G.f.: 1/(1-2*x+2*x^2).
%C A099087 Yet another variation on A009545.
%C A099087 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.
%C A099087 Binomial transform of A057077. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Nov 04 2008]
%C A099087 Partial sums of A146559 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Dec 01 2008]
%H A099087 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%F A099087 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).
%F A099087 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
%F A099087 a(n)=Sum_{k, 0<=k<=n} A109466(n,k)*2^k. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Oct 28 2008]
%o A099087 (Other) sage: [lucas_number1(n,2,2) for n in xrange(1, 50)] # [From Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Apr 23 2009]
%Y A099087 Cf. A009545.
%Y A099087 Sequence in context: A100240 A072690 A108520 this_sequence A009545 A084102 
               A160125
%Y A099087 Adjacent sequences: A099084 A099085 A099086 this_sequence A099088 A099089 
               A099090
%K A099087 easy,sign
%O A099087 0,2
%A A099087 Paul Barry (pbarry(AT)wit.ie), Sep 24 2004
%E A099087 Signs added by N. J. A. Sloane (njas(AT)research.att.com), Nov 14, 2006

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