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Search: id:A100887
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| A100887 |
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Expansion of (-1+2x+2x^2)/((1+x+x^2)(1-x-x^2)). |
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+0
3
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| -1, 2, 1, 0, 4, 4, 5, 12, 17, 26, 46, 72, 115, 190, 305, 492, 800, 1292, 2089, 3384, 5473, 8854, 14330, 23184, 37511, 60698, 98209, 158904, 257116, 416020, 673133, 1089156, 1762289, 2851442, 4613734, 7465176, 12078907, 19544086, 31622993, 51167076
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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This sequence was investigated in cooperation with Paul Barry. Generating floretion: - 0.5'i - 0.5'k - 0.5j' - 0.5'ii' + 0.5'jj' - 0.5'kk' + 0.5'ik' - 0.5'ki' ("les").
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FORMULA
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a(n) = Fib(n+1)/2-sqrt(3)cos(2pi*n/3+pi/6); a(n)=a(n-2)+2a(n-3)+a(n-4), a(0) = -1, a(1) = 2, a(2) = 1, a(3) = 0
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MATHEMATICA
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a[n_] := Fibonacci[n + 1]/2 - Sqrt[3]Cos[2Pi*n/3 + Pi/6]; Table[ a[n], {n, 0, 39}]
a[0] = -1; a[1] = 2; a[2] = 1; a[3] = 0; a[n_] := a[n] = a[n - 2] + 2a[n - 3] + a[n - 4]; Table[ a[n], {n, 0, 39}]
CoefficientList[ Series[(-1 + 2x + 2x^2)/((1 - x - x^2)(1 + x + x^2)), {x, 0, 39}], x] (from Robert G. Wilson v Dec 02 2004)
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PROGRAM
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Floretion Algebra Multiplication Program
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CROSSREFS
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Cf. A100886, A100888, A100889, A100890.
Sequence in context: A052922 A109167 A066426 this_sequence A073592 A077929 A086095
Adjacent sequences: A100884 A100885 A100886 this_sequence A100888 A100889 A100890
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KEYWORD
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sign
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AUTHOR
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Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Nov 21 2004
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EXTENSIONS
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Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 02 2004
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