%I #21 Apr 03 2024 03:26:26
%S 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,
%T 147,49,31,128,328,652,792,1240,792,652,328,128,708,1719,3717,6735,
%U 7281,7281,6735,3717,1719,708,4015,10320,28585,43780,58120,73240,58120,43780,28585,10320,4015
%N 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.
%C 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).
%H Ludovic Schwob, <a href="/A365094/b365094.txt">Table of n, a(n) for n = 3..1481</a>
%H Ludovic Schwob, <a href="/A365094/a365094.pdf">Illustration of T(6,k), 0<=k<=6</a>
%F T(n,0) = T(n,n) = A295264(n).
%e Triangle begins:
%e 1, 0, 0, 1;
%e 1, 0, 4, 0, 1;
%e 2, 5, 5, 5, 5, 2;
%e 9, 12, 21, 36, 21, 12, 9;
%e 31, 49, 147, 133, 133, 147, 49, 31;
%Y Row sums give A000142(n-1) (number of cycles of length n).
%Y Cf. A295264, A342968, A008292.
%K nonn,tabf
%O 3,7
%A _Ludovic Schwob_, Aug 21 2023