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Search: id:A113874
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| A113874 |
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a(3n) = a(3n-1) + a(3n-2), a(3n+1) = 2n*a(3n) + a(3n-1), a(3n+2) = a(3n+1) + a(3n). |
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+0
3
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| 1, 0, 1, 1, 3, 4, 7, 32, 39, 71, 465, 536, 1001, 8544, 9545, 18089, 190435, 208524, 398959, 4996032, 5394991, 10391023, 150869313, 161260336, 312129649, 5155334720, 5467464369, 10622799089, 196677847971, 207300647060
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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A113873(n)/a(n) -> e.
Without the first two terms, same as A007677 (denominators of convergents to e). - Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Aug 16 2006
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REFERENCES
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H. Cohn, A short proof of the simple continued fraction expansion of e, Amer. Math. Monthly, 113 (No. 1, 2006), 57-62.
J. Sondow, A geometric proof that e is irrational and a new measure of its irrationality, Amer. Math. Monthly 113 (2006) 637-641.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..201
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MAPLE
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a[0]:=1: a[1]:=0: a[2]:=1: for n from 3 to 34 do if n mod 3 = 0 then a[n]:=a[n-1]+a[n-2] elif n mod 3 = 1 then a[n]:=2*(n-1)*a[n-1]/3+a[n-2] else a[n]:=a[n-1]+a[n-2] fi: od: seq(a[n], n=0..34); (Deutsch)
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MATHEMATICA
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a[0] = 1; a[1] = 0; a[n_] := a[n] = Switch[ Mod[n, 3], 0, a[n - 1] + a[n - 2], 1, 2(n - 1)/3*a[n - 1] + a[n - 2], 2, a[n - 1] + a[n - 2]]; a /@ Range[0, 30]
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CROSSREFS
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Cf. A113873.
Sequence in context: A041091 A117764 A007677 this_sequence A042773 A042173 A046461
Adjacent sequences: A113871 A113872 A113873 this_sequence A113875 A113876 A113877
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KEYWORD
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easy,nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Jan 27 2006
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(at)rgwv.com) and Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 28 2006
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