Tribonacci rectangle

 It is observed that the side of a square of the geometric series equals the sum of the three immediately preceding.
For this you can tend to the golden rectangle building appropriate rectangles with square in the following sequence:

1, 1, 2, 4, 7, 13, 24, 44, 81, 149, 274, 504, 927, 1705, 3136, 5768, 10609, 19513, 35890, 66012, 121415, 223317..

Ratio of two consecutive numbers of the sequence tends to the relationship between major and minor side of the rectangle tribonacci:


1,83928675...       one of the solution of    r³-r²-r-1=0
 

Start of rectangles identified by square building with sides according to the tribonacci sequence

Shortly after the result is confused with the tribonacci rectangle to which it tends

packing and unpacking