A358329 Triangle read by rows: T(n,k) is the number of polygons with 2*n sides, of which k run through the center of a circle, on the circumference of which the 2*n vertices of the polygon are arranged at equal spacing, up to rotation and reflection.

0, 0, 1, 1, 0, 1, 4, 3, 3, 2, 70, 60, 54, 12, 6, 2980, 3512, 2088, 704, 156, 28, 268444, 315840, 176928, 59204, 13488, 1920, 193, 36387789, 42112416, 22965696, 7722144, 1759104, 277344, 28992, 1743, 6789078267, 7716280320, 4153217280, 1393136640, 321814080, 53061120, 6216960, 483840, 20640

Offset

0,7

Comments

By "2*n-sided polygons" we mean the polygons that can be drawn by connecting 2*n equally spaced points on a circle.

T(0,0)=0 and T(0,1)=1 by convention.

The sequence is limited to even-sided polygons, since all odd-sided polygons have no side passing through the center.

Links

Ludovic Schwob, Table of n, a(n) for n = 0..5150

Example

Triangle begins:
    0;
    0,   1;
    1,   0,   1;
    4,   3,   3,   2;
   70,  60,  54,  12,   6;

Crossrefs

Row sums give A094157(n).

Cf. A330662.

Sequence in context: A305743 A117691 A243564 * A171627 A239884 A143487

Adjacent sequences: A358326 A358327 A358328 * A358330 A358331 A358332

Keyword

nonn,tabl

Author

Ludovic Schwob, Nov 09 2022

Status

approved