OFFSET
0,5
LINKS
Alois P. Heinz, Antidiagonals n = 0..200, flattened
FORMULA
Starting with T(n, 0) = 1, if (k-n) is negative or even then T(n, k) = 2*T(n, k-1), otherwise T(n, k) = 2*T(n, k-1) - A061897(n+1, (k-n-1)/2). So for n>=k, T(n, k) = 2^k. [Corrected by Sean A. Irvine, Mar 23 2024]
T(n,0) = 1, T(n,k) = (2^k/(n+1))*Sum_{r=1..n+1} (-1)^r*cos((Pi*(2*r-1))/(2*(n+1)))^k*cot((Pi*(1-2*r))/(4*(n+1))). - Herbert Kociemba, Sep 23 2020
EXAMPLE
Rows start:
1, 0, 0, 0, 0, ...
1, 2, 2, 4, 4, ...
1, 2, 4, 6, 12, ...
1, 2, 4, 8, 14, ...
...
MATHEMATICA
T[n_, 0]=1; T[n_, k_]:=2^k/(n+1) Sum[(-1)^r Cos[(Pi (2r-1))/(2 (n+1))]^k Cot[(Pi (1-2r))/(4 (n+1))], {r, 1, n+1}]; Table[T[r, n-r], {n, 0, 20}, {r, 0, n}]//Round//Flatten (* Herbert Kociemba, Sep 23 2020 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Henry Bottomley, Mar 06 2002
STATUS
approved