A276669 Triangle read by rows T(n,k) in which row n lists the first 2n-1 nonnegative integers representing 2n-1 equidistant points labeled in counterclockwise direction around a circle, with the 0th point at the top and reading them from left to right.

0, 1, 0, 2, 1, 2, 0, 3, 4, 2, 1, 3, 0, 4, 6, 5, 2, 3, 1, 4, 0, 5, 8, 6, 7, 3, 2, 4, 1, 5, 0, 6, 10, 7, 9, 8, 3, 4, 2, 5, 1, 6, 0, 7, 12, 8, 11, 9, 10, 4, 3, 5, 2, 6, 1, 7, 0, 8, 14, 9, 13, 10, 12, 11, 4, 5, 3, 6, 2, 7, 1, 8, 0, 9, 16, 10, 15, 11, 14, 12, 13, 5, 4, 6, 3, 7, 2, 8, 1, 9, 0, 10, 18, 11, 17, 12, 16, 13, 15, 14

Offset: 1

Author

James Bentley and Omar E. Pol, Sep 12 2016

Keywords

• nonn
• tabf
• look

Examples

			Triangle begins:
0;
1, 0, 2;
1, 2, 0, 3, 4;
2, 1, 3, 0, 4, 6, 5;
2, 3, 1, 4, 0, 5, 8, 6, 7;
3, 2, 4, 1, 5, 0, 6, 10, 7, 9, 8;
3, 4, 2, 5, 1, 6, 0, 7, 12, 8, 11, 9, 10;
4, 3, 5, 2, 6, 1, 7, 0, 8, 14, 9, 13, 10, 12, 11;
4, 5, 3, 6, 2, 7, 1, 8, 0, 9, 16, 10, 15, 11, 14, 12, 13;
5, 4, 6, 3, 7, 2, 8, 1, 9, 0, 10, 18, 11, 17, 12, 16, 13, 15, 14;
...
Illustration of numbers around a circle associated to the fourth row of triangle:
.
.               0
.           1       6
.
.          2         5
.
.             3   4
.
So the 4th row of the triangle is [2, 1, 3, 0, 4, 6, 5].
		

Links

• James Bentley, Rows 0...405 flattened

Crossrefs

Column 1 is A110654. Middle diagonal is A000004. Apart from the first term, right border gives A001651.

Cf. A001477, A004526.

Programs

Mathematica

f[n_] := Transpose[ Sort[ Table[{Sin[ 2i*Pi/n + Pi], i}, {i, 0, n -1}], #1[[1]] < #2[[1]] &]][[2]]; Table[ f[n], {n, 1, 19, 2}] // Flatten (* Robert G. Wilson v, Nov 18 2016 *) (* Changing the constant in the Mmca coding changes where the reading begins. Pi starts it at the 9 o'clock position, Pi/2 would start it at the 12 o'clock position, 0 would have it start at the 3 o'clock position, etc. *)