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Triangle T(n,k) = sum_{j=k..n} Fibonacci(n-j+1)*Fibonacci(k+1), read by rows, 0<=k<=n.
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%I #5 Sep 17 2013 13:21:39

%S 1,2,1,4,2,2,7,4,4,3,12,7,8,6,5,20,12,14,12,10,8,33,20,24,21,20,16,13,

%T 54,33,40,36,35,32,26,21,88,54,66,60,60,56,52,42,34,143,88,108,99,100,

%U 96,91,84,68,55,232,143,176,162,165,160,156,147,136,110,89

%N Triangle T(n,k) = sum_{j=k..n} Fibonacci(n-j+1)*Fibonacci(k+1), read by rows, 0<=k<=n.

%F Matrix product of T(n,k) = sum_j A104762(n+1,j)*A104763(j+1,k), both interpreted as lower triangular square arrays.

%e The first few rows of the triangle are:

%e 1;

%e 2, 1;

%e 4, 2, 2;

%e 7, 4, 4, 3;

%e 12, 7, 8, 6, 5;

%e 20, 12, 14, 12, 10, 8

%Y Cf. A000071 (1st and 2nd column), A019274 (3rd column)

%K nonn,tabl

%O 0,2

%A _Gary W. Adamson_, Mar 20 2005

%E Incorrect conjecture on row sums removed. _R. J. Mathar_, Sep 17 2013