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 A113874 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). 3
 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; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS A113873(n)/a(n) -> e. Without the first two terms, same as A007677 (denominators of convergents to e). - Jonathan Sondow, Aug 16 2006 LINKS T. D. Noe, Table of n, a(n) for n = 0..201 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. J. Sondow, A geometric proof that e is irrational and a new measure of its irrationality, arXiv:0704.1282 [math.HO], 2007-2010. J. Sondow and K. Schalm, Which partial sums of the Taylor series for e are convergents to e? (and a link to the primes 2, 5, 13, 37, 463), II, Gems in Experimental Mathematics (T. Amdeberhan, L. A. Medina, and V. H. Moll, eds.), Contemporary Mathematics, vol. 517, Amer. Math. Soc., Providence, RI, 2010. MAPLE 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); # Emeric Deutsch, Jan 28 2006 MATHEMATICA 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] Join[{1, 0}, Denominator[Convergents[E, 30]]] (* Harvey P. Dale, Aug 09 2014 *) CROSSREFS Cf. A113873. Sequence in context: A041091 A270373 A117764 * A007677 A042773 A042173 Adjacent sequences: A113871 A113872 A113873 * A113875 A113876 A113877 KEYWORD easy,nonn AUTHOR N. J. A. Sloane, Jan 27 2006 EXTENSIONS More terms from Robert G. Wilson v and Emeric Deutsch, Jan 28 2006 STATUS approved

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Last modified April 15 20:47 EDT 2024. Contains 371696 sequences. (Running on oeis4.)