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Search: id:A100888
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| A100888 |
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Expansion of (3+x-x^2)/((1+x+x^2)(1-x-x^2)). |
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3
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| 3, 1, 2, 7, 7, 12, 23, 33, 54, 91, 143, 232, 379, 609, 986, 1599, 2583, 4180, 6767, 10945, 17710, 28659, 46367, 75024, 121395, 196417, 317810, 514231, 832039, 1346268, 2178311, 3524577, 5702886, 9227467, 14930351, 24157816, 39088171, 63245985
(list; graph; listen)
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OFFSET
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0,1
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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' ("jes"). A100885(n) = (1/2)(A100886(n) + A100887(n) - a(n))
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FORMULA
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a(n) = Fib(n+2)+sqrt(3)cos(2pi*n/3 + pi/6)+sin(2pi*n/3 + pi/6); a(n)=a(n-2)+2a(n-3)+a(n-4), a(0) = 3, a(1) = 1, a(2) = 2, a(3) = 7
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MATHEMATICA
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a[0] = 3; a[1] = 1; a[2] = 2; a[3] = 7; a[n_] := a[n] = a[n - 2] + 2a[n - 3] + a[n - 4]; Table[ a[n], {n, 0, 37}] (from Robert G. Wilson v Nov 26 2004)
CoefficientList[ Series[(3 + x - x^2)/((1 + x + x^2)(1 - x - x^2)), {x, 0, 37}], x] (from Robert G. Wilson v Nov 26 2004)
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PROGRAM
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Floretion Algebra Multiplication Program
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CROSSREFS
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Cf. A100885, A100886, A100887, A100889, A100890.
Adjacent sequences: A100885 A100886 A100887 this_sequence A100889 A100890 A100891
Sequence in context: A151855 A135338 A084602 this_sequence A052914 A131671 A060750
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KEYWORD
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nonn
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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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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 26 2004
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