A365094 Triangle read by rows: T(n,k) is the number of n-sided cycles with the property that one makes k turns to the right while following its edges.

1, 0, 0, 1, 1, 0, 4, 0, 1, 2, 5, 5, 5, 5, 2, 9, 12, 21, 36, 21, 12, 9, 31, 49, 147, 133, 133, 147, 49, 31, 128, 328, 652, 792, 1240, 792, 652, 328, 128, 708, 1719, 3717, 6735, 7281, 7281, 6735, 3717, 1719, 708, 4015, 10320, 28585, 43780, 58120, 73240, 58120, 43780, 28585, 10320, 4015

Offset

3,7

Comments

Cycles that differ by rotation or reflection are counted separately. By "n-sided cycles" we mean the cycles that can be drawn by connecting n equally spaced points on a circle (possibly self-intersecting).

Links

Ludovic Schwob, Table of n, a(n) for n = 3..1481

Ludovic Schwob, Illustration of T(6,k), 0<=k<=6

Formula

T(n,0) = T(n,n) = A295264(n).

Example

Triangle begins:
   1,   0,   0,   1;
   1,   0,   4,   0,   1;
   2,   5,   5,   5,   5,   2;
   9,  12,  21,  36,  21,  12,   9;
  31,  49, 147, 133, 133, 147,  49,  31;

Crossrefs

Row sums give A000142(n-1) (number of cycles of length n).

Cf. A295264, A342968, A008292.

Sequence in context: A071637 A141277 A198637 * A179296 A196817 A229987

Adjacent sequences: A365091 A365092 A365093 * A365095 A365096 A365097

Keyword

nonn,tabf

Author

Ludovic Schwob, Aug 21 2023

Status

approved