A164846 Triangle read by rows: frequency with which the number of values taken by cos(2*Pi/k) mod j occurs for each j >= 1, taken over k = 1..j-1.

0, 0, 1, 0, 1, 1, 0, 2, 1, 0, 0, 1, 3, 0, 0, 0, 3, 0, 0, 1, 1, 0, 2, 3, 0, 1, 0, 0, 0, 4, 0, 0, 2, 0, 0, 1, 0, 3, 1, 1, 2, 0, 1, 0, 0, 0, 3, 2, 0, 1, 2, 0, 0, 1, 0, 0, 2, 5, 1, 1, 0, 1, 0, 0, 0, 0, 0, 6, 0, 0, 3, 0, 0, 0, 0, 0, 0, 2, 0, 3, 6, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 5, 2, 0, 2, 1, 0, 0, 1, 2, 0, 0, 0, 0

Offset: 1

Author

Christopher Hunt Gribble, Aug 28 2009

Keywords

• nonn
• tabl

Comments

See A164823 for explanatory comment and the definition of "cos(x) mod j".

Examples

			The triangle of numbers is:
..j....Frequency of numbers of solutions over k
.......0..1..2..3..4..5..6..7..8..9..10
..1....0
..2....0..1
..3....0..1..1
..4....0..2..1..0
..5....0..1..3..0..0
..6....0..3..0..0..1..1
..7....0..2..3..0..1..0..0
..8....0..4..0..0..2..0..0..1
..9....0..3..1..1..2..0..1..0..0
.10....0..3..2..0..1..2..0..0..1..0
.11....0..2..5..1..1..0..1..0..0..0..0
		

Links

• Christopher Hunt Gribble, Flattened triangle, for j = 1..100 and k = 1..j-1.

Crossrefs

Cf. A164822, A164823, A164831, A165252.

Extensions

Minor edits from N. J. A. Sloane, Sep 01 2009

Sequence corrected by Christopher Hunt Gribble, Sep 10 2009

Minor edits by Christopher Hunt Gribble, Oct 01 2009