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Search: id:A088137
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| A088137 |
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Generalized Gaussian Fibonacci integers. |
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+0
8
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| 0, 1, 2, 1, -4, -11, -10, 13, 56, 73, -22, -263, -460, -131, 1118, 2629, 1904, -4079, -13870, -15503, 10604, 67717, 103622, 4093, -302680, -617639, -327238, 1198441, 3378596, 3161869, -3812050, -17109707, -22783264, 5762593, 79874978, 142462177, 45299420, -336787691
(list; graph; listen)
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OFFSET
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0,3
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LINKS
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C. Dement, The Math Forum.
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FORMULA
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a(n)=3^(n/2)sin(n*atan(sqrt(2))/sqrt(2)
|3*A087455(n) - A087455(n+1)| = 2*a(n+1) or 3*A087455(n) + A087455(n+1) = 2*a(n+1). - Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Aug 02 2004
a(n+1) = tes(x^n) = -les(x^n)/3 x= 2('i) - 'k - 'jj' - 'ji' - 'jk' - 1. - Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Aug 02 2004
G.f.: x/(1-2x+3x^2); E.g.f.: exp(x)sin(sqrt(2)x)/sqrt(2); a(n)=2a(n-1)-3a(n-2), a(0)=0, a(1)=1; a(n)=((1+i*sqrt(2))^n-(1-i*sqrt(2))^n)/(2i*sqrt(2)); a(n)=Im{(1+i*sqrt(2))^n/sqrt(2)}; a(n)=sum{k=0..floor(n/2), C(n, 2k+1)(-2)^k}.
3^(n+1)= 9*(A087455(n))^2 + 2*(A087455(n+1))^2 - 2*(a(n+2))^2; 3^n = (a(n+1))^2 + 3(a(n))^2 - 2*a(n+1)*a(n), n > 0 - Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Jan 20 2005
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PROGRAM
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(Other) sage: [lucas_number1(n, 2, 3) for n in xrange(0, 38)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 23 2009]
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CROSSREFS
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Cf. A084102, A088138, A045873, A088139.
Cf. A087455.
Sequence in context: A016544 A134028 A111479 this_sequence A064297 A052661 A088624
Adjacent sequences: A088134 A088135 A088136 this_sequence A088138 A088139 A088140
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KEYWORD
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easy,sign
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Sep 20 2003
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