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Search: id:A113873
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| A113873 |
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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, 1, 2, 3, 8, 11, 19, 87, 106, 193, 1264, 1457, 2721, 23225, 25946, 49171, 517656, 566827, 1084483, 13580623, 14665106, 28245729, 410105312, 438351041, 848456353, 14013652689, 14862109042, 28875761731, 534625820200
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Without the first two terms, same as A007676 (numerators 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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FORMULA
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a(n)/A113874(n) -> e.
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MAPLE
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a[0]:=1: a[1]:=1: a[2]:=2: for n from 3 to 33 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..33); (Deutsch)
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MATHEMATICA
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a[0] = a[1] = 1; 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] (* Robert G. Wilson v *)
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CROSSREFS
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Sequence in context: A041075 A041893 A007676 this_sequence A042443 A042263 A153439
Adjacent sequences: A113870 A113871 A113872 this_sequence A113874 A113875 A113876
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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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