OFFSET
1,1
COMMENTS
Let R denote a rectangle whose shape (i.e., length/width) is (7+sqrt(105))/4. This rectangle can be partitioned into squares in a manner that matches the continued fraction [4,3,4,1,4,3,4,1...]. It can also be partitioned into rectangles of shape 3/2 and 3 so as to match the continued fraction [7/2, 1, 7/2, 1, ...]. For details, see A188635.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..10000
EXAMPLE
4.311737691489899595805259670130262997684...
MATHEMATICA
FromContinuedFraction[{7/2, 1, {7/2, 1}}]
ContinuedFraction[%, 25] (* [4, 3, 4, 1, 4, 3, 4, 1...] *)
RealDigits[N[%%, 120]] (* A189968 *)
N[%%%, 40]
PROG
(PARI) (7+sqrt(105))/4 \\ G. C. Greubel, Jan 12 2018
(Magma) (7+Sqrt(105))/4 // G. C. Greubel, Jan 12 2018
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, May 05 2011
STATUS
approved