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Search: id:A123005
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| A123005 |
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Scaled Recursion, coefficient expansion and Binet for a "Tin mean": Characteristic polynomial :l = 2; m = 7; x^2-l*x/m-1. |
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+0
1
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| 0, 1, 2, 53, 204, 3005, 16006, 179257, 1142808, 11069209, 78136010, 698663261, 5225991012, 44686481813, 345446523214, 2880530655265, 22687940948016, 186521884004017, 1484752874460818, 12109078065118469, 96971046978817020
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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l=2; m=3; gives A002534
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REFERENCES
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Jay Kappraff, Beyond Measure, A Guided Tour Through Nature, Myth and Number, World Scientific, 2002.
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FORMULA
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l = 2; m = 7; a(n) = l*a(n - 1)/m + a(n - 2) C.F.=x/(1 - 2 x/7 - x^2)
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MATHEMATICA
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(* coefficient expansion*) l = 2; m = 7; p[x_] := -1 - l*x/m + x^2 q[x_] := ExpandAll[x^2*p[1/x]] Table[ SeriesCoefficient[ Series[x/q[x], {x, 0, 30}], n]*m^(n - 1), {n, 0, 30}] (* Binet/ recursion *) f[n_Integer] = Module[{a}, a[n] /. RSolve[{a[n] == l*a[n - 1]/m + a[n - 2], a[0] == 0, a[1] == 1}, a[n], n][[1]] // FullSimplify] ; a = Table[Rationalize[N[f[n]*m^(n - 1), 100], 0], {n, 0, 25}]
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CROSSREFS
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Cf. A002534.
Sequence in context: A041337 A139844 A130698 this_sequence A142477 A119112 A109791
Adjacent sequences: A123002 A123003 A123004 this_sequence A123006 A123007 A123008
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KEYWORD
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nonn,uned
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AUTHOR
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Roger Bagula and Gary Adamson (rlbagulatftn(AT)yahoo.com), Sep 23 2006
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