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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.

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