A239748 Number of distinct sequences defined by the elements of powers >= 0 of n X n (0,1) matrices.

2, 13, 132, 3833, 363288

Offset: 1

Author

Christopher Hunt Gribble, Mar 26 2014

Keywords

• nonn
• hard
• more

Examples

			a(2) = 13 because there are 13 distinct sequences in the set of 256 sequences formed by each element of each 2 X 2 binary matrix raised to successive powers >= 0.  The first 10 terms of the distinct sequences and the frequencies of occurrence are:
Sequence                                Frequency
0, 0, 0, 0, 0,  0,  0,  0,   0,   0, ...       16
0, 1, 0, 0, 0,  0,  0,  0,   0,   0, ...        2
0, 1, 0, 1, 0,  1,  0,  1,   0,   1, ...        2
0, 1, 1, 1, 1,  1,  1,  1,   1,   1, ...        4
0, 1, 1, 2, 3,  5,  8, 13,  21,  34, ...        4
0, 1, 2, 3, 4,  5,  6,  7,   8,   9, ...        2
0, 1, 2, 4, 8, 16, 32, 64, 128, 256, ...        2
1, 0, 0, 0, 0,  0,  0,  0,   0,   0, ...       12
1, 0, 1, 0, 1,  0,  1,  0,   1,   0, ...        2
1, 0, 1, 1, 2,  3,  5,  8,  13,  21, ...        2
1, 1, 1, 1, 1,  1,  1,  1,   1,   1, ...       12
1, 1, 2, 3, 5,  8, 13, 21,  34,  55, ...        2
1, 1, 2, 4, 8, 16, 32, 64, 128, 256, ...        2
.                                        Total 64
		

Links

• Christopher Hunt Gribble, C++ Program

Crossrefs

Cf. A238596.