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Triangle read by rows: T(n,m) = gcd(Fibonacci(n), Fibonacci(m)).
0

%I #15 Aug 02 2019 22:44:49

%S 0,1,1,1,1,1,2,1,1,2,3,1,1,1,3,5,1,1,1,1,5,8,1,1,2,1,1,8,13,1,1,1,1,1,

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

%U 55

%N Triangle read by rows: T(n,m) = gcd(Fibonacci(n), Fibonacci(m)).

%C Row sums are {0, 2, 3, 6, 9, 14, 22, 32, 51, 78, 123, ...}.

%C T(n,m) = Fibonacci(gcd(n,m)).

%e Table begins

%e 0;

%e 1, 1;

%e 1, 1, 1;

%e 2, 1, 1, 2;

%e 3, 1, 1, 1, 3;

%e 5, 1, 1, 1, 1, 5;

%e 8, 1, 1, 2, 1, 1, 8;

%e 13, 1, 1, 1, 1, 1, 1, 13;

%e 21, 1, 1, 1, 3, 1, 1, 1, 21;

%e 34, 1, 1, 2, 1, 1, 2, 1, 1, 34;

%e 55, 1, 1, 1, 1, 5, 1, 1, 1, 1, 55;

%t Flatten[Table[Table[GCD[Fibonacci[n], Fibonacci[m]], {m, 0, n}], {n, 0, 10}]]

%Y Cf. A000045.

%K nonn,tabl

%O 0,7

%A _Roger L. Bagula_, Nov 28 2010