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A006281 Partial quotients in continued fraction expansion of 2C-1, where C is Cahen's constant.
(Formerly M2260)
6

%I M2260 #22 Mar 19 2024 03:20:09

%S 0,3,2,18,98,33282,319994402,354455304050635218,

%T 36294953231792713902640647988908098

%N Partial quotients in continued fraction expansion of 2C-1, where C is Cahen's constant.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Amiram Eldar, <a href="/A006281/b006281.txt">Table of n, a(n) for n = 0..12</a>

%H J. L. Davison and Jeffrey O. Shallit, <a href="https://doi.org/10.1007/BF01332350">Continued Fractions for Some Alternating Series</a>, Monatshefte für Mathematik, Vol. 111 (1991), pp. 119-126; <a href="http://gdz.sub.uni-goettingen.de/dms/load/img/?PPN=PPN362162050_0111&amp;DMDID=DMDLOG_0013&amp;LOGID=LOG_0013&amp;PHYSID=PHYS_0126">alternative link</a>.

%t s[0] = 2; s[n_] := s[n] = s[n - 1]^2 - s[n-1] + 1; h[0] = 1; h[n_] := h[n] = (s[n] - 1)/(2*h[n-1]); a[0] = 0; a[1] = 3; a[n_] := 2*h[n-1]^2; Array[a, 9, 0] (* _Amiram Eldar_, Mar 19 2024 *)

%Y Cf. A006279, A006280, A118227.

%K nonn,easy,changed

%O 0,2

%A _N. J. A. Sloane_.

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Last modified March 29 03:51 EDT 2024. Contains 371264 sequences. (Running on oeis4.)