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A006280 Partial quotients in continued fraction expansion of Cahen's constant.

%I A006280 M3372 #39 Jul 08 2025 16:45:40
%S A006280 0,1,1,1,4,9,196,16641,639988804,177227652025317609,
%T A006280 72589906463585427805281295977816196,
%U A006280 2280022876287160141646375873338796324543839666085098409289740769448641
%N A006280 Partial quotients in continued fraction expansion of Cahen's constant.
%C A006280 Shifted squares of denominators of convergents to Cahen's constant: a(n) = A006279(n-2)^2 for n > 1. - _Jonathan Sondow_, Aug 20 2014
%D A006280 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A006280 Amiram Eldar, <a href="/A006280/b006280.txt">Table of n, a(n) for n = 0..14</a>
%H A006280 Khalil Ayadi, Chiheb Ben Bechir, and Maher Saadaoui, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL28/Ayadi/ayadi12.html">Continued Fractions with Predictable Patterns and Transcendental Numbers</a>, J. Int. Seq. (2025) Vol. 28, Art. No. 25.1.4.
%H A006280 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 A006280 b[n_] := b[n] = If[n < 2, 1, b[n-2]^2*b[n-1] + b[n-2]];
%t A006280 a[n_] := If[n == 0, 0, b[n-2]^2];
%t A006280 Table[a[n], {n, 0, 10}] (* _Jean-François Alcover_, Sep 23 2022, after _Jonathan Sondow_ *)
%Y A006280 Cf. A006279, A006281, A118227.
%K A006280 nonn,easy
%O A006280 0,5
%A A006280 _N. J. A. Sloane_