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

1,4

Links

James Bentley, Rows 0...405 flattened

Example

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].

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. *)

Crossrefs

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

Cf. A001477, A004526.

Sequence in context: A344788 A068076 A138498 * A307596 A240205 A340732

Adjacent sequences: A276666 A276667 A276668 * A276670 A276671 A276672

Keyword

nonn,tabf,look

Author

James Bentley and Omar E. Pol, Sep 12 2016

Status

approved