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Triangle T(j,k) = remainder of Fibonacci(j) divided by Fibonacci(k), for 3 < j and 2 < k < j.
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%I #3 Mar 30 2012 17:27:38

%S 1,1,2,0,2,3,1,1,3,5,1,0,1,5,8,0,1,4,2,8,13,1,1,0,7,3,13,21,1,2,4,1,

%T 11,5,21,34,0,0,4,0,1,18,8,34,55,1,2,3,1,12,2,29,13,55,89,1,2,2,1,0,

%U 20,3,47,21,89,144,0,1,0,2,12,1,32,5,76,34,144,233,1,0,2,3,12,0,1,52,8,123

%N Triangle T(j,k) = remainder of Fibonacci(j) divided by Fibonacci(k), for 3 < j and 2 < k < j.

%C The zero values T(j,1) and T(j,2) have been omitted, so the first row consists of T(4,3). - A072523(n) = sum(T(n,k), k = 3, ..., n-1) for n > 3.

%e a(0) = Fibonacci(4) mod Fibonacci(3) = 3 mod 2 = 1; a(2) = Fibonacci(5) mod Fibonacci(4) = 5 mod 3 = 2.

%o (PARI) for(j=4,16, for(k=3,j-1,print1(fibonacci(j)%fibonacci(k),",")))

%Y Cf. A072523.

%K easy,nonn,tabl

%O 0,3

%A _Klaus Brockhaus_, Aug 01 2002