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Array read by antidiagonals, T(n,k) = 2*(n/k) - 1, if n mod k = 0; otherwise, T(n,k) = 1.
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%I #9 Jun 29 2020 05:09:15

%S 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,

%T 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,

%U 23,1,1,1,1,1,1,1,1,1,1,1,25,11,1,1,1,1

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

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

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

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

%e Array begins

%e 1 1 1 1 1 ...

%e 3 1 1 1 1 ...

%e 5 1 1 1 1 ...

%e 7 3 1 1 1 ...

%e 9 1 1 1 1 ...

%e .............

%t 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 *)

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

%K cofr,nonn,tabl

%O 1,2

%A _Ross La Haye_, Dec 05 2009

%E More terms from _Amiram Eldar_, Jun 29 2020