OFFSET
1,2
COMMENTS
Decimal expansion of the shape of a Catalan-extension rectangle; see A188640 for definitions of shape and r-extension rectangle.
Specifically, for a Catalan-extension rectangle, 1 square is removed first, then 1 square, then 1 square again, then 3 squares, then 1 square, ... (see A320640), so that the original rectangle is partitioned into an infinite collection of squares.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..10000
Clark Kimberling, Two kinds of golden triangles, generalized to match continued fractions, Journal for Geometry and Graphics, 11 (2007) 165-171.
EXAMPLE
1.557868355876025567309823249177... = [Catalan, Catalan, Catalan, ...]
MAPLE
evalf((Catalan+sqrt(4+Catalan^2))/2, 135);
MATHEMATICA
First@ RealDigits[(Catalan + Sqrt[4 + Catalan^2])/2, 10, 105] (* Michael De Vlieger, Oct 23 2018 *)
PROG
(PARI) (Catalan+sqrt(4+Catalan^2))/2 \\ Felix Fröhlich, Oct 23 2018
(Magma) R:= RealField(200); (Catalan(R) + Sqrt(4 + Catalan(R)^2)) / 2; // Vincenzo Librandi, Oct 24 2018
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Paolo P. Lava, Oct 18 2018
STATUS
approved