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A Fibonacci triangle: T(n,k) = Fib(k+2) for 0 <= k <= n.
2

%I #18 Mar 02 2023 10:22:26

%S 1,1,2,1,2,3,1,2,3,5,1,2,3,5,8,1,2,3,5,8,13,1,2,3,5,8,13,21,1,2,3,5,8,

%T 13,21,34,1,2,3,5,8,13,21,34,55,1,2,3,5,8,13,21,34,55,89,1,2,3,5,8,13,

%U 21,34,55,89,144,1,2,3,5,8,13,21,34,55,89,144,233

%N A Fibonacci triangle: T(n,k) = Fib(k+2) for 0 <= k <= n.

%C n-th row sum: A001911, Fib(n+3)-2;

%C n-th alternating row sum: A000045, F(n).

%C The augmentation (as defined at A193091) of A193588 is A193589.

%F a(n) = A115346(n) + 1. - _Filip Zaludek_, Nov 19 2016

%e First 5 rows of A193588:

%e 1;

%e 1, 2;

%e 1, 2, 3;

%e 1, 2, 3, 5;

%e 1, 2, 3, 5, 8;

%t (See A193589, the augmentation of A193588.)

%t Table[Fibonacci[k+2],{n,0,20},{k,0,n}]//Flatten (* _Harvey P. Dale_, Nov 29 2017 *)

%t Module[{nn=15,fibs},fibs=Fibonacci[Range[2,nn]];Table[Take[fibs,n],{n,nn-1}]]// Flatten (* _Harvey P. Dale_, Mar 02 2023 *)

%Y Cf. A193588.

%K nonn,tabl

%O 0,3

%A _Clark Kimberling_, Jul 31 2011