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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.
2
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).
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).
Sequence in context: A071637 A141277 A198637 * A179296 A196817 A229987
KEYWORD
nonn,tabf
AUTHOR
Ludovic Schwob, Aug 21 2023
STATUS
approved