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Triangle T(n,k) = Fibonacci(n+k), related to A000045 (Fibonacci numbers).
3

%I #21 Apr 07 2023 18:30:12

%S 0,1,1,1,2,3,2,3,5,8,3,5,8,13,21,5,8,13,21,34,55,8,13,21,34,55,89,144,

%T 13,21,34,55,89,144,233,377,21,34,55,89,144,233,377,610,987,34,55,89,

%U 144,233,377,610,987,1597,2584

%N Triangle T(n,k) = Fibonacci(n+k), related to A000045 (Fibonacci numbers).

%F T(n,0) = Fibonacci(n) = A000045(n),

%F T(n,n) = Fibonacci(2n) = A001906(n),

%F T(2n,n) = Fibonacci(3n) = A014445(n).

%F T(n,k) = T(n,k-1) + T(n-1,k-1) = T(n-1,k-1) + T(n-1,k).

%e Triangle begins :

%e 0;

%e 1, 1;

%e 1, 2, 3;

%e 2, 3, 5, 8;

%e 3, 5, 8, 13, 21;

%e 5, 8, 13, 21, 34, 55;

%e 8, 13, 21, 34, 55, 89, 144;

%e 13, 21, 34, 55, 89, 144, 233, 377;

%e ...

%Y Cf. A000045, A001906, A014445.

%Y Row sums give A362067.

%K easy,nonn,tabl

%O 0,5

%A _Philippe Deléham_, Nov 07 2011