A006280 - OEIS

%I M3372 #31 Mar 19 2024 03:20:13

%S 0,1,1,1,4,9,196,16641,639988804,177227652025317609,

%T 72589906463585427805281295977816196,

%U 2280022876287160141646375873338796324543839666085098409289740769448641

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

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

%H Amiram Eldar, <a href="/A006280/b006280.txt">Table of n, a(n) for n = 0..14</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 b[n_] := b[n] = If[n < 2, 1, b[n-2]^2*b[n-1] + b[n-2]];

%t a[n_] := If[n == 0, 0, b[n-2]^2];

%t Table[a[n], {n, 0, 10}] (* _Jean-François Alcover_, Sep 23 2022, after _Jonathan Sondow_ *)

%Y Cf. A006279, A006281, A118227.

%K nonn,easy

%O 0,5

%A _N. J. A. Sloane_.