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Search: id:A100886
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| A100886 |
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Expansion of x(1+3x+2x^2)/((1+x+x^2)(1-x-x^2)). |
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3
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| 0, 1, 3, 3, 5, 10, 14, 23, 39, 61, 99, 162, 260, 421, 683, 1103, 1785, 2890, 4674, 7563, 12239, 19801, 32039, 51842, 83880, 135721, 219603, 355323, 574925, 930250, 1505174, 2435423, 3940599, 6376021, 10316619, 16692642, 27009260, 43701901
(list; graph; listen)
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OFFSET
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0,3
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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' ("tes"). (1/2)(a(n) + A100887(n) - A100888(n)) gives A061347(n+3).
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FORMULA
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a(n) = (L(n+1)-A061347(n))/2, L=A000032; a(n)=a(n-2)+2a(n-3)+a(n-4), a(0) = 0, a(1) = 1, a(2) = 3, a(3) = 3
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MATHEMATICA
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a[0] = 0; a[1] = 1; a[2] = 3; a[3] = 3; a[n_] := a[n] = a[n - 2] + 2a[n - 3] + a[n - 4]; Table[ a[n], {n, 0, 36}]
(* Or *) CoefficientList[ Series[x(1 + 3x + 2x^2)/((1 + x + x^2)(1 - x - x^2)), {x, 0, 36}], 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. A087204, A100887, A100888, A100889, A100890.
Sequence in context: A000198 A027170 A132775 this_sequence A072337 A132751 A032020
Adjacent sequences: A100883 A100884 A100885 this_sequence A100887 A100888 A100889
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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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