A238596 Number of distinct sequences defined by the upper left value in powers of n X n (0,1) matrices.

2, 6, 50, 1140, 86052

Offset: 1

Author

Jay Anderson, Mar 01 2014

Keywords

• hard
• more
• nonn

Comments

A sequence can be defined by powers of a matrix with only 0 and 1 values. For instance, the upper left value in the matrix M^n where M=[0 1; 1 1] is the Fibonacci sequence.

Also, the number of distinct sequences defined by all element values in powers of n X n (0, 1) matrices (see A239748) that start with 1. - Christopher Hunt Gribble, May 12 2014

Examples

			a(2) = 6 since there are 6 distinct sequences for 2 X 2 (0,1) matrices:
[0 0; 0 0] => 0 0 0 0 0 ...
[1 0; 0 0] => 1 1 1 1 1 ...
[0 1; 0 0] => 0 0 0 0 0 ...
[1 1; 0 0] => 1 1 1 1 1 ...
[0 0; 1 0] => 0 0 0 0 0 ...
[1 0; 1 0] => 1 1 1 1 1 ...
[0 1; 1 0] => 0 1 0 1 0 ...
[1 1; 1 0] => 1 2 3 5 8 ...
[0 0; 0 1] => 0 0 0 0 0 ...
[1 0; 0 1] => 1 1 1 1 1 ...
[0 1; 0 1] => 0 0 0 0 0 ...
[1 1; 0 1] => 1 1 1 1 1 ...
[0 0; 1 1] => 0 0 0 0 0 ...
[1 0; 1 1] => 1 1 1 1 1 ...
[0 1; 1 1] => 0 1 1 2 3 ...
[1 1; 1 1] => 1 2 4 8 16 ...
		

Crossrefs

Cf. A239748.