

A276669


Triangle read by rows T(n,k) in which row n lists the first 2n1 nonnegative integers representing 2n1 equidistant points labeled in counterclockwise direction around a circle, with the 0th point at the top and reading them from left to right.


2



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
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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: A272569 A068076 A138498 * A307596 A240205 A050319
Adjacent sequences: A276666 A276667 A276668 * A276670 A276671 A276672


KEYWORD

nonn,tabf,look


AUTHOR

James Bentley and Omar E. Pol, Sep 12 2016


STATUS

approved



