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 A104862 First differences of A014292. 13
 0, 1, 1, 1, 1, 0, -2, -5, -9, -13, -15, -12, 0, 25, 65, 117, 169, 196, 158, 3, -321, -841, -1519, -2200, -2560, -2079, -79, 4121, 10881, 19720, 28638, 33435, 27351, 1547, -52895, -140772, -256000, -372775, -436655, -359763, -26871 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 COMMENTS Real part of the sequence of complex numbers defined by c(n) = c(n-1) + i*c(n-2) for n > 1, c(0) = 1, c(1) = 1. 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). LINKS Michael De Vlieger, Table of n, a(n) for n = 0..6285 FORMULA G.f.: Re(1/(1-x-ix^2)) = (1-x)/(1-2x+x^2+x^4). - Paul Barry, Apr 25 2005 a(n) = Sum_{k=0..floor(n/2)} C(n-k, k)*cos(Pi*k/2). - Paul Barry, Apr 25 2005 a(0)=0, a(1)=1, a(n+1) = a(n) - Sum_{k=0..n-3} a(k). - Alex Ratushnyak, May 03 2012 MATHEMATICA Differences@ LinearRecurrence[{2, -1, 0, -1}, {0, 0, 1, 2}, 42] (* Michael De Vlieger, Mar 19 2021 *) PROG (Python) a = [0]*1000 a[1]=1 for n in range(1, 55): print(a[n-1], end=", ") s=sum(a[k] for k in range(n-2)) a[n+1] = a[n]-s # from Alex Ratushnyak, May 03 2012 CROSSREFS Cf. A078001, A014292. Sequence in context: A270950 A139405 A360899 * A190686 A247986 A259252 Adjacent sequences: A104859 A104860 A104861 * A104863 A104864 A104865 KEYWORD sign AUTHOR Gerald McGarvey, Apr 24 2005 STATUS approved

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Last modified June 21 03:10 EDT 2024. Contains 373535 sequences. (Running on oeis4.)