A338849 - OEIS

%I #28 Dec 23 2020 17:36:38

%S 1,1,1,1,2,0,1,3,0,0,1,4,4,0,0,1,5,10,0,0,10,1,6,18,12,24,60,36,1,7,

%T 28,42,112,280,420,322,1,8,40,96,336,1040,2400,3696,2832,1,9,54,180,

%U 792,3060,9540,22428,35280,27954,1,10,70,300,1600,7540,29880,95340,229280,369540,299260

%N Triangle read by rows: T(n,k) is the number of permutations of k elements from [1..n] in a circle where adjacent values cannot be consecutive modulo n, rotations are distinct

%C In a convex n-gon, the number of paths using k-1 diagonals and k non-repeated vertices, start and end vertices are not connected by a side.

%F T(n,k) = n*(A338526(n-1,k-1)-2*S(n-1,k-1)+Z2(n-1,k-1)) for k>0 except T(2,2)=0, T(n,0)=1, where Z2(n,k) = Z1(n,k) except Z2(n,1)=2, where Z1(n,k) = S(n-1,k-1)-Z(n-1,k-1) for k>0 except Z1(2,2)=0, Z1(n,0)=0, where S(n,k) = 2*A338526(n-1,k-1)-S(n-1,k-1) for k>0, S(n,0)=0.

%e n\k  0    1    2    3    4    5    6    7    8

%e 0    1

%e 1    1    1

%e 2    1    2    0

%e 3    1    3    0    0

%e 4    1    4    4    0    0

%e 5    1    5    10   0    0    10

%e 6    1    6    18   12   24   60   36

%e 7    1    7    28   42   112  280  420  322

%e 8    1    8    40   96   336  1040 2400 3696 2832

%Y Cf. A011973, A034807, A338526, A338838, A000166.

%K nonn,tabl

%O 0,5

%A _Xiangyu Chen_, Nov 12 2020