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

0, 1, 1, 1, 4, 9, 196, 16641, 639988804, 177227652025317609, 72589906463585427805281295977816196, 2280022876287160141646375873338796324543839666085098409289740769448641

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Shifted squares of denominators of convergents to Cahen's constant: a(n) = A006279(n-2)^2 for n > 1. - Jonathan Sondow, Aug 20 2014

References

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

Links

• Amiram Eldar, Table of n, a(n) for n = 0..14
• Khalil Ayadi, Chiheb Ben Bechir, and Maher Saadaoui, Continued Fractions with Predictable Patterns and Transcendental Numbers, J. Int. Seq. (2025) Vol. 28, Art. No. 25.1.4.
• J. L. Davison and Jeffrey O. Shallit, Continued Fractions for Some Alternating Series, Monatshefte für Mathematik, Vol. 111 (1991), pp. 119-126; alternative link.

Crossrefs

Cf. A006279, A006281, A118227.

Programs

Mathematica

b[n_] := b[n] = If[n < 2, 1, b[n-2]^2*b[n-1] + b[n-2]];
a[n_] := If[n == 0, 0, b[n-2]^2];
Table[a[n], {n, 0, 10}] (* Jean-François Alcover, Sep 23 2022, after Jonathan Sondow *)