A171232 Array read by antidiagonals, T(n,k) = 2*(n/k) - 1, if n mod k = 0; otherwise, T(n,k) = 1.

1, 3, 1, 5, 1, 1, 7, 1, 1, 1, 9, 3, 1, 1, 1, 11, 1, 1, 1, 1, 1, 13, 5, 1, 1, 1, 1, 1, 15, 1, 3, 1, 1, 1, 1, 1, 17, 7, 1, 1, 1, 1, 1, 1, 1, 19, 1, 1, 1, 1, 1, 1, 1, 1, 1, 21, 9, 5, 3, 1, 1, 1, 1, 1, 1, 1, 23, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 25, 11, 1, 1, 1, 1

Offset: 1

Author

Ross La Haye, Dec 05 2009

Keywords

• cofr
• nonn
• tabl

Comments

T(n,1): continued fraction expansion of coth(1).

T(n,2): continued fraction expansion of tan(1) = cot(pi/2 - 1).

Examples

			Array begins
1 1 1 1 1 ...
3 1 1 1 1 ...
5 1 1 1 1 ...
7 3 1 1 1 ...
9 1 1 1 1 ...
.............
		

Crossrefs

Cf. T(n, 1) = A005408(n-1), T(n, 2) = A093178(n-1), A171233, A077049.

Programs

Mathematica

T[n_,k_] := If[Divisible[n, k], 2*(n/k) - 1, 1]; Table[T[n-k+1, k], {n, 1, 10}, {k,1, n}] //Flatten (* Amiram Eldar, Jun 29 2020 *)

Formula

T(n,k) = A171233(n,k) - A077049(n,k).

Extensions

More terms from Amiram Eldar, Jun 29 2020