A006280 Partial quotients in continued fraction expansion of Cahen's constant. (Formerly M3372)

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

Offset

0,5

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

J. L. Davison and Jeffrey O. Shallit, Continued Fractions for Some Alternating Series, Monatshefte für Mathematik, Vol. 111 (1991), pp. 119-126; alternative link.

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 *)

Crossrefs

Cf. A006279, A006281, A118227.

Sequence in context: A354305 A080438 A029999 * A290158 A202463 A286322

Adjacent sequences: A006277 A006278 A006279 * A006281 A006282 A006283

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved