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 A104862 First differences of A014292. 12

%I

%S 0,1,1,1,1,0,-2,-5,-9,-13,-15,-12,0,25,65,117,169,196,158,3,-321,-841,

%T -1519,-2200,-2560,-2079,-79,4121,10881,19720,28638,33435,27351,1547,

%U -52895,-140772,-256000,-372775,-436655,-359763,-26871

%N First differences of A014292.

%C Real part of the sequence of complex numbers defined by c(0) = 1, c(1) = 1, for n>1 c(n) = c(n-1) + i*c(n-2).

%C a(n) = real part of the sequence b of quaternions defined by b(0)=1,b(1)=1, b(n) = b(n-1) + b(n-2)*(0,s,s,s) where s = 1/sqrt(3).

%F G.f.: Re(1/(1-x-ix^2))=(1-x)/(1-2x+x^2+x^4). - _Paul Barry_, Apr 25 2005

%F a(n)=sum{k=0..floor(n/2), C(n-k, k)cos(pi*k/2)}; - _Paul Barry_, Apr 25 2005

%F a(0)=0, a(1)=1, a(n+1) = a(n) - Sum_{k=0..n-3} a(k). - _Alex Ratushnyak_, May 03 2012

%o (Python)

%o a = [0]*1000

%o a[1]=1

%o for n in range(1,55):

%o . print a[n-1],

%o . sum=0

%o . for k in range(n-2):

%o . . sum+=a[k]

%o . a[n+1] = a[n]-sum

%o # from _Alex Ratushnyak_, May 3 2012

%Y Cf. A078001, A014292.

%K sign

%O 0,7

%A _Gerald McGarvey_, Apr 24 2005

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Last modified May 24 10:57 EDT 2013. Contains 225619 sequences.